Input-output Ratio & Technology Life-Cycle

4. RESOURCE MANAGEMENT
Q.No.1. Write a short note on - Input-output Ratio.
Input-output Ratio: Input-output analysis reflects a general theory of production based on the idea of
economic interdependence. Many input - output models are useful in forecasting. Input - output analysis
takes into consideration the inter dependence of the different sectors in the economy. This is because; the
input to one sector is output of another sector. For example, the output of coal industry will be an input to
the steel plant and the output of steel industry is an input to the construction industry and so on. There are
many such cyclic relations within the various sectors of economy. Taking the data of outputs and inputs
and studying the relationship between these two, we will be in a position to analyse the total demand for a
product and the output required from industrial units. This type of analysis is very important because it
takes into account all the intricate relationships in the economy.
Three major assumptions in developing this technique are:
1. The total output of an industry is consumed as input by all industries for a time period, under
consideration.
2. The input bought by each industry has usually been made dependent only on the industry’s level of
output.
3. The ration of an industry’s input to its output, once established is fixed. This ratio is known as input
output number or production coefficient.
Q.No.2 Write a short note on Technology Life-Cycle. (J 05, D 07 - 3M)
Technology Life-Cycle: Like a product has its life cycle, technology also has a life cycle. The various
phases or stages in a technology life cycle are:
a. Innovation in which stage a new technology (product or process technology) is
developed,
b. Syndication during which stage, the technology is demonstrated and slowly
commercialised,
c. Diffusion stage in which a new technology gradually replaces the current
technology and
d. Substitution stage in which the current technology becomes obsolete and is
completely replaced by the new technology.
Q.No.3 Expand& briefly Explain the following in the context of Technology used to enhance
Production. (a) AGV, (b) AIS (D 08 - 4M)
Automated Guided Vehicles (AGVs): These are automated materials handling and delivery systems
which can take the form of mono-rails, conveyors, driverless trains, pallet trucks and unit load carriers.
AGVs are electronically guided and controlled vehicles used to move parts and equipments. AGVs usually
follow either embedded guide wires or paint strips through operations until their destinations are reached.
Automated Identification Systems (AIS): These use bar codes, radio frequencies, magnetic stripes,
optical character recognition and machine vision to sense and input data into computers. These systems
replace human beings to read data from products, documents, parts and containers and interpret the data.
An example is the system used to identify and read the bar code on an item in the check-out counters at
grocery stores. A scanner reads the identification number from the bar code on the item accesses a
ICWA Inter_ 1e_ Operation Management _ Resource Management_____________ 4.1
No.1 for CA/CWA & MEC/CEC
MASTER MINDS

computer data base, and sends the price of the item to the cash register and updates the ;inventory data
in the inventory system.
Q.No.4 Expand the following system of Production Technology. Narrate the main feature related to
enhancement of Production and advantages divided from the System. (a) FMS, (b) CIM (J 09 - 8M)
a. Flexible Manufacturing System (FMS): A flexible manufacturing system (FMS) is a configuration of a
group of production machines (or workstations) connected by automated material handling and
transferring machines and integrated by computer system which can give instructions to produce
hundreds of different parts in whatever order specified.
Features:
• Several computers controlled machining centres or workstations having CNC machines and
robots
• For loading and unloading.
• Computer controlled transport system (AGVs) for moving materials and parts from one machine
to
• Another and in and out of the system.
• Computer controlled robots for loading and unloading stations.
• An automated storing and retrieval system.
Advantages
a. Improved capital utilization, b. Lower direct labour cost,
c. Reduced inventory, d. Consistent quality,
e. Improved productivity.
b. Computer Integrated Manufacturing (CIM): Computer Integrated Manufacturing is a system which
acts as a bridge or umbrella to integrate product design and engineering, process planning and
manufacturing using complex computer systems.
• Computer-Aided-Design facilitates the design of the product, its quality analysis, planning the
manufacturing process, designing tools and. fixtures and machine loading programs.
• Computer-Aided-Manufacturing allows fabrication of raw materials into parts to be sent to the
assembly lines.
• Automated Storage and Retrieval System (ASRS) and automated guided vehicles (AGVs)
facilitate storage/retrieval, movement of incoming materials and parts, work-in-process and finished
products
Q.No.5 Briefly Explain Advantages of N/C Machines. (J 09 - 2M)
Numerical Control: Many machines such as lathe, milling, drilling and boring machines are now designed
for electronic control called numerical control (NC). The numerically controlled (NC) machines have control
systems which read instructions and translate them into machine operations.
Advantages of N/C Machines:
• Smaller machine setup time
• Machine motions and tool changing are controlled by instructions on a control system
• Increased productivity and higher quality
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• Suitable for low volume production.
Q.No.6 Expand the term CIM and write the implication of adopting CIM: (D 09 - 1+2 = 3M)
CIM: Computer Integrated Manufacturing
Implication of adopting CIM: Computer Integrated Manufacturing is a system which acts as a bridge or
umbrella to integrate product design and engineering, process planning and manufacturing using complex
computer systems.
a. Computer-Aided-Design facilitates the design of the product, its quality analysis,
planning the manufacturing process, designing tools and. fixtures and machine loading programs.
b. Computer-Aided-Manufacturing allows fabrication of raw materials into parts to
be sent to the assembly lines.
c. Automated Storage and Retrieval System (ASRS) and automated guided
vehicles (AGVs) facilitate storage/retrieval, movement of incoming materials and parts, work-in-process
and finished products
Q.No.7 Mention the advantages of the following advertisements in Production Technology
(a) Robots (b) FMS (J 11 - 3+3 = 6M)
a. Robots: Robotics or robotry is a fast developing field of technology in which human like machines
perform production tasks. A robot is a reprogrammable, multifunctional manipulator designed to move
materials, parts, tools or specialised devices through variable programmed motions for the
performance of a variety of tasks.
Advantages:-
• do not strike work,
• do not mind hot, dirty, dusty working conditions,
• can work at high speeds,
• will not sue if injured,
• can work long hours without breaks
• can be used for welding, painting, assembly work, loading, unloading, material handling and other
repetitive, monotonous work.
b. Flexible Manufacturing System (FMS): A flexible manufacturing system (FMS) is a configuration of a
group of production machines (or workstations) connected by automated material handling and
transferring machines and integrated by computer system which can give instructions to produce
hundreds of different parts in whatever order specified.
Advantages:-
• Improved capital utilization
• Lower direct labour cost
• Reduced inventory
• Consistent quality
• Improved Productivity
Q.No.8 Expand & Explain the following (a) CNC, (b) APC, (c) VS, (d) ASRS, (e) AFL, (f) AAS,(g) ERP
a. CNC: When these machines are programmed through their own minicomputers and have memories to
store these programs, they are called computer numerical control (CNC) machines.
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Advantages of N/C Machines:
• Smaller machine setup time
• Machine motions and tool changing are controlled by instructions on a control
system
• Increased productivity and higher quality
• Suitable for low volume production.
b. Automated Process Control (APC): Automated process control makes use of information technology
to monitor and control a physical process. It is also used to determine and control temperatures,
pressures and quantities in petroleum refineries, cement plants, chemical plants, steel mills, nuclear
reactors etc. Vision systems are also used for visual inspection in food processing organizations.
Automated inspection systems facilitate 100 percent inspection which will lead to improved product
quality and reduced inspection costs.
c. Vision Systems (VS) (Automated Inspection Systems): These are machines or equipments that
have been integrated into the inspection of products for controlling quality. They combine video
camera and computing technology to take physical dimensions of parts, compare the measurements
to standards and determine whether the parts meet quality specifications
d. Automated Storage and Retrieval Systems (ASRS): Computer controlled warehouses use ASRS;
which provide for the automatic placement and withdrawal of parts and products into and from
designated storage places in the warehouse. Such systems are commonly used in distribution facilities
of retailers.
e. Automated Flow Lines (AFL): An automated flow line includes several automated machines which
are linked by automated transfer machines and handling machines. The raw material feeders
automatically feed the individual machines and operations are carried out without human intervention.
After an item is machined on one machine on the line, the partially completed item is automatically
transferred to the next machine on the line in a predetermined sequence, until the job is completed.
f. Automated Assembly Systems (AAS): In this system automated assembly machines or equipments
are linked together by automated materials handling equipments. Examples of automated assembly
equipments are robotic welders or component insertion unit which are used to join one or more parts
or components or assemblies.
g. Enterprise Resource Planning (ERP) System: ERP systems comprise latest comprehensive
software packages to automate a number of business processes. This software integrates most of the
business functions in an organization. ERP systems have automated manufacturing processes,
organized account books, streamlined corporate departments such as human resources and facilitate
business process re-engineering.
ERP systems need complex set of software programs and heavy investment to implement them.
Several ERP software packages have been developed by leading software companies such as SAP,
Oracle, J.D. Edwards, People Soft and Baan. The latest development in ERP system has been the
integration of e-business capabilities.
E-business uses the internet to conduct or facilitate business transactions such as sales, purchasing,
communication, inventory management, customer service, placing purchase orders and checking the
status of purchase orders etc. ERP software packages were modified with additional features to
facilitate e-business.
h. Computer Aided Design (CAD): It is an electronic system using computers for designing new parts
or products or modifying existing ones, replacing the traditional drafting work done by a draftsman on a
drafting board. The CAD consists of a powerful desktop computer and graphics software that enables
a designer to manipulate geometric shapes. The designer can create drawings and view them from
any angle on a display monitor. CAD softwares have been developed for designing electronic circuits,

printed-circuit-board design, designing and drafting three dimensional drawings and also for analysis
of heat and stress in mechanical designs.
Advantages of CAD are:
• Allows designers to save time and money by shortening design and development cycle
time,
• Eliminates prototype model building to prove the design,
• Allows designers to determine costs and test such variable as stress, tolerance, product
variability, interchangeability and serviceability,
• Low cost of design even for a custom-built, low volume product,
• Eliminates manual drafting completely,
• Makes review of numerous options in design possible before final commitments are made
because of the speed and ease with which sophisticated designs can be manipulated,
• Faster development, better products and accurate flow of information to other departments
• Product cost can be determined at the design stage itself.
Q.No.9 Explain the concept of Replacement of Machine?
Replacement of Machines and Equipment: Machines are purchased and replacement of old machines-
are made mainly for two reasons:
a. To increase the productive capacity and
b. To reduce cost of production.
Various other reasons for replacement are the following:
a. To get rid of worn out, broken down or obsolete machines,
b. To accommodate larger sizes of work and increase the machine capacity,
c. To reduce labour cost by introducing semi-automatic machines or machines
more than one of which can be operated by a single operator,
d. To simplify operations by using automatic machines which are capable of
performing variety of work usually performed by a number of different machines,
e. To minimize repair cost and reduce idle time.
An analysis of the above six reasons will lead to either increase in capacity or reduction in cost or both.
Q.No.10 Explain the meaning of a Linear Programming Problem?
1. Meaning: A Linear Programming Problem (LPP) is a mathematical model dealing with the use
allocation of certain scare resources (i e key factor like raw materials, labour hours, machine time,
capital availability, etc.)in the possible manner in order to maximize profit or minimize cost.
2. Conditions: LPP consists of a particular class of programming problems, which should meet the
following conditions
a. Variables: There must be decision variables e.g. products, time, processes etc. which the
decision - maker may use at different levels. These must be non – negative. These decision
variables may be denoted by alphabets like a, b, c, etc. or x1, x2, x3, etc.
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b. Objective: There must be a defined objective, i.e. either maximization of profit or minimization of
cost. The objective function is denoted by Z. The objective function should be defined by use of a
linear function involving the decision variables.
c. Constraints: There should be limitations / restrictions relating to the use of certain resources.
These constraints are denoted by inequations having ≤or ≥sign. In some cases, the conditions
can be stated using ‘ =’ sign also.
Q.No.11 List the areas of LPP application
1. Industrial Applications - production planning, product - mix, blending, trim applications, etc.
2. Product Distribution - transportation applications.
3. Marketing Applications - Advertising mix problems.
4. Financial Applications - investment portfolio.
5. Administrative Applications - personnel assignment, balancing production, inventories and work - force.
6. Agriculture Applications.
7. Operational Scheduling Applications - Flight scheduling applications.
Q.No.12 What are the disadvantages of LPP?
1. Existence of non - linear equations: The primary requirement of linear programming is that the
objective function and constraint function should be linear. Practically, linear relationships do not exist
in all cases.
2. Interaction between variables: LP fails in a situation where non - linearity in the equations emerge
due to joint interactions between some of the activities like total measure of effectiveness or total
usage of some resource.
3. Fractional Values: In LPP, fractional values are permitted for the decision variables. However, many
decision problems require the solution for decision variable to be in non - fractional values. Rounding -
off the values obtained by LP techniques may not result in an optimal solution in such cases.
4. Knowledge of co - efficient of the equations: It may not be possible to state all co - efficients in the
objective function and constraints with certainty. Also, variables in most cases are random variables
with an individual probability distribution for the values.
Q.No.13. What is Degeneracy in a Simplex LLP? How is it resolved? (J 10 - 2+2 = 4M)
Degeneracy Method: Sometimes, it happens that during the course of simplex procedure, we get two or
more entries in the ratio column of any tableau to be identical and minimum. Now, the question arises
which row should. be taken as key row? The selection of key row determines the variable to be deleted.
This is known as degeneracy. The problem of degeneracy may also occur when one of the constraints on
the right hand side of the equation is zero.
The degeneracy is resolved by the following procedure:
1. Each element of the row which have identical entries in the ratio column is divided by the key column
number of the respective row.
2. The values so obtained are compared step by step from left to right. Priority is to be given to identify
columns corresponding to slack and artificial variables. The remaining columns are considered from
left t right.
3. The comparison is stopped as soon as the rows yield unequal ratios. The row having algebraically
smaller ratio is taken to be the key row.

After selecting the key row, regular simplex procedure is resumed.
Q.No.14 Explain what is a slack variable under simplex Method of linear Programming? (D 11 - 2M)
A Slack variable represents costless Process whose function is to “use” up’ otherwise unused capacity,
say, machine time or warehouse capacity. Effectually, the slack variable represents unused capacity, and
it will be zero, only if production facilities or capacities are fully utilized, in each constrained equation, the
variables used in other equations are also introduced but with zero coefficients. The same slack variables
are also introduced in the objectives function but by the time it is maximum, all their coefficient will be zero.
Slack variables are always non-negative.
Q.No.15 In relation to linear Programming explain “Dul Problem”? (D 04 - 5M)
The term dual in general sense implies two or double. In the context of linear programming, duality implies
that each linear programming problem can be analyzed in two different ways but having equivalent
solution. Each linear programming problem (both maximization and minimization) stated in its original form
has associated with another linear programming problem (called dual linear programming problem or in
short dual), which is unique, based on the same data. In general, it is immaterial which of the two
problems is called primal or dual, since the dual of the dual is primal.
PROBLEMS
Problem1: A company has 3 factories and 3 customers. The following table gives the transportation cost
per unit from the factories to the customers and also the quantities available and required. Determine the
initial transportation solution using Vogel’s method. (D 09 - 4M)
Factory A B C Availability
F1 10 11 20 10
F2 15 12 10 2
F3 17 9 16 8
Requirement 8 5 7 20
Problem2: The following table shows all the necessary information on the availability of supply to each
factory of BEST Industries Ltd., the requirement of each destination and the unit transport cost (in/ Rs )
from each factory to each destination: (J 04 - 10M)
Factory Destination Supply
I II III
A 5 1 7 10
B 6 4 6 80
C 3 2 5 15
Demand 75 20 50
Since there is not enough supply, some of the demands at the three destinations may not be satisfied. For
the unsatisfied demands, let the penalty costs be Re.1, Rs.2 and Rs.3 respectively.
Find the optimal allocation that minimizes the transportation and penalty costs by using the Vogel’s
Approximation Method (VAM).
Problem 3: A Company has four factories Fl, F2, F3 and F4 manufacturing the same product. Production
and raw material costs differ from factory to factory and are given in the following table. The transportation
costs from the factories to sales depots S1, S2 and S3 are also given. The sales price and the total
MASTER MINDS

requirement at each depot as also the product capacity at each factory is also stated. Determine the most
profitable production and distribution schedule and the corresponding profit. The surplus production
should be taken to yield zero profit.
(ICWA - M)
Particulars F1 F2 F3 F4
Sales price per
unit
Requirements
per unit
Production Cost
per unit
15 18 14 13
Raw material Cost
per unit
10 9 12 9
Transportation
cost per unit to
S1 3 9 5 4 34 80
S2 1 7 4 5 32 120
S3 5 8 3 6 31 150
Production
capacity (units)
10 150 50 100
Problem 4: A company has three factories and four customers. It furnishes the following schedule of profit
per unit on transportation of goods to customers in rupees. You are required to solve the transportation
problem to maximize the profit. Determine the resultant optimal profit. (ICWA - M)
Factory / Customer A B C D Supply
P 40 25 22 33 100
Q 44 35 30 30 30
R 38 38 28 30
Demand 40 20 60 30
Problem 5: X Company is interested in taking loans from banks for its projects — P, Q, R, S, T. The rates of
interest and the lending capacity differ from bank to bank. All these projects are to be completed. The
relevant details are provided below. Assuming the role of a consultant, advice the Company as to how it
should take the loans so that the total interest payable is least. Find out alternate optimum solutions, if any.
(ICWA - M)
Source Bank
Interest rate in % for projects Max Credit
P Q R S T (in 000s)
Private Bank 20 18 18 17 17 Any Amount
Nationalised Bank 16 16 16 15 16 400
Co-operative Bank 15 15 15 13 14 250
Amount required (in 000s) 200 150 200 125 75
Problem 6: The information on the available supply to each warehouse, requirement of each market and
the unit transportation cost from each warehouse to each market is given below: (ICWA - M)
Warehouse
Market Supply
M1 M2 M3 M4
A 5 2 4 3 22
B 4 8 1 6 15
C 4 6 7 5 8
Demand 7 12 17 9
The shipping clerk has worked out the following schedule from his experience:

Units 12 1 9 15 7 1
From
warehouse
A A A B C C
To – market M2 M3 M4 M3 M1 M3
You are required to:
a. Check and see if the clerk has the optimal schedule.
b. Find the optimal schedule and minimum total shipping cost and If the clerk is
approached by a carrier of route C to M2, who offers to reduce his rate in the hope of getting some
business, by how much should the rate be reduced before the clerk considers giving him an order.
Problem 7: The following table gives the running costs per year and resale values of a certain equipment
whose purchase price is Rs. 6,500. At what year is the replacement due optimally. (ICWA - M)
Year 1 2 3 4 5 6 7 8
Running
costs (Rs.)
1,400 1,500 1,700 2,000 2,400 2,800 3,300 3,900
Resale value
(Rs.)
4,000
3,000
2,200 1,700 1,300 1,000 1,000 1,000
Problem 8: A Plant Manager is considering replacement policy to a new machine. He estimates the
following costs: (ICWA - M)
Year 1 2 3 4 5 6
Replacemen
t cost at the
beginning of
the year
100 110 125 140 160 190
Salvage
value at the
end of the
year
60 50 40 25 10 0
Operating
costs
25 30 40 50 65 80
Find the year when replacement is to be made.
Problem 9: Replacement policy is being considered for a new machine installed. Find the year when the
replacement is to be made based on the following information: (J 10 - 3M)
Year 1 2 3 4 5
Replacement cost at
beginning of the year
1,700 2,000 2,500 2,850 3,000
Salvage value at the end
of the year
1,175 1,200 900 400 0
Operating Costs 500 700 750 1,100 1,200
Problem 10: A truck-owner finds from his past experience that the maintenance costs are Rs. 200 for the
first year and then increase by Rs. 2,000 every year. The cost of the Truck Type A is Rs. 9,000. Determine
the best age at which to replace, i.e. truck. If the optimum replacement is followed what will be the average
yearly cost of owing and operating the Truck? Truck Type B cost Rs. 10,000. Annual operating costs are
Rs. 400 for the first year and then increase by Rs. 800 every year. The Truck owner have now the Truck
Type A which is one year old. Should it be replaced with B type, and if so, when? (ICWA - M)
MASTER MINDS

Problem 11: A fleet owner finds from his past records that the costs per year of running a vehicle whose
purchase price is Rs 50,000 are as under: (ICWA - M)
Year 1 2 3 4 5 6 7
Running
cost Rs.)
5,000 6,000 7,000 9,000 11,500 16,000 18,000
Resale
value (Rs.)
30,000 15,000 7,500 3,750 2,000 2,000 2,000
Thereafter, running cost increases by Rs. 2,000, but resale value remains constant at Rs. 2,000. At what
age is a replacement due?
Problem 12: A manufacturer is offered two machines A and B. A is priced at Rs. 5,000 and running costs
are estimated Rs. 800 for each of the first five years, increasing by Rs. 200 per year in the sixth and
subsequent year. Machine B, which has the same capacity as A, costs Rs. 2,500 but will have running
costs of Rs. 1,200 per year for six years, increasing by Rs. 200 per year thereafter. If money is worth 10%
per year, which machine should be purchased? (Assume that the machines will eventually be sold for
scrap at a negotiable price). (ICWA - M)
Problem 13: The following mortality rates have been observed for a certain type of light bulbs: (ICWA - M)
Week 1 2 3 4 5
Per cent failing by end of week 10 25 50 80 100
There are 1,000 bulbs in sue, and it costs Rs. 2 to replace an individual bulb which has burnt out. If all
bulbs were replaced simultaneously it would cost 50 paise per bulb. It is proposed to replace all bulbs at
fixed intervals, whether or not they have burnt out, and to continue replacing burnt out bulbs as they fail.
At what intervals should all the bulbs be replaced?
Problem 14: Suppose that a special purpose type of light bulb never lasts longer than 2 weeks. There is a
chance of 0.3 that a bulb will fail at the end of the first week. There are 100 new bulbs initially. The cost
per bulb for individual replacement is Re. 1 and the cost per bulb for a group replacement is Re. 0.50. It is
cheapest to replace all bulbs: (i) individually, (ii) every week, (iii) every second week, (iv) every third week?
(ICWA - M)
Problem 15: A key electric component lasts for a maximum of 3 weeks. The chances of its failing at the
end of first week is 0.1 and the chance of its failing at the end of second week is 0.3.The cost per
component for individual replacement is 5 and cost per component for bulk replacement is Rs. 3. What is
the optimal replacement period assuming there are 100 components initially? (D 08 - 4M)
Problem 16: Solve by Simplex Method: (ICWA - M)
Maximize= 321 3x2x-x + , Subject to 9x+3x+x 321 ≤ , 8x+2x+-x 321 ≤ , 0x,x,x 321 ≥
Problem17: A gear manufacturing company makes two types of gears an-A and B.both gears are
processed on 3 machines, Hobbing M/c, Shaping M/c, Griding M/c the time required by each gear and
total time available per week on each machine is as follows: (ICWA
- M)
Gera (A) (Hours) Gear (B) (Hours) Available Hours
Machine
Hobbing M/c 3 3 36
Shaping M/c 5 2 60
Griding M/c 2 6 60
Other data:

Selling Price (Rs.) 820 960
Variable (Rs) 780 900
Determine the optimum Production plan and maximum contribution for the next week by simplex method.
The initial table is given below
Problem 18: Find the non-negative values of X1 X2 and X3 that maximize the expression (ICWA - M)
Z= 221 4x5x3x ++
Subject to the following restraints 83x+2x 21 ≤ , 105x+2x 21 ≤ , 15x42x+3x 221 ≤+
Problem 19: Find the maximum value of Z= 221 4x5x3x ++ . Where 0x,x,x 321 ≥ , subject to the
following constraints.
(ICWA - M)
18x32x 21 ≤+ , 18x52x 22 ≤+ , 25x4x23x 321 ≤++
Problem 20:-Maximise 21 x23x + under the following restrictions: (ICWA -
M)
0x0,>x 21 ≥ , 40x2x 21 ≤+ , 24xx 21 ≤+ , 60x32x 21 ≤+
Problem 21:- A company manufactures two items X1 and X2. They are sold at a profit of Rs. 30 per unit of X1
and Rs. 20 per unit of X2. X1 requires 2kgs of materials, 3 man-hours and 1 machine hour per unit. X2 requires 1
kg of material, 2 man hours and 3 machine hours per unit. (ICWA -
M)
During each production run there are 280 kgs of material available, 500 labour hours and 420 hours of
machines used. How much of the two items should the company produce to maximize profits?
Problem 22: An animal feed company must produce 200 kg. of a mixture consisting of ingredients X and
Y daily. X costs Rs. 3 per kg. and Y Rs. 8 per kg. No more than 80 kgs. of X can be used and at least 60
kgs. of Y must be used. Formulate the problem as a Linear Programming Model. (D 05 - 6M)
Problem 23: Optimax Mutual Fund Company has Rs. 30 lakhs available for investment in Government
bonds, Blue chip stocks, Speculative stocks and Short term deposits. The annual expected return and risk
factor are given below: (J 07 - 2M)
Type of investment
Annul Expected
Return(%)
Risk Factor
(0 to 100)
Government bonds 12 12
Blue Chip Stocks 20 24
Speculative Stocks 24 48
Short term deposits 10 6
Mutual Fund is required to keep at least 4 lakhs in short term deposits and not to exceed average risk
factor of 42. Speculative stocks must be at most 20% of the total amount invested.
How should OPTIMAX MUTUAL FUND Company invest the funds so as to maximise its total expected
annual return? Formulate this as a Linear Programming Problem. You are not required to solve the LPP.
Problem 24: Four products A, B, C and D have Rs. 5, Rs.7, Rs. 3 and Rs. 9 profitability respectively. First
type of material (limited supply of 800 kg) is required by A, B, C and D at 4 kg, 3 kg, 8 kg and 2 kg,
respectively per unit. Second type of material has a limited supply of 300 kg, and is for A, B, C arid D at 1
kg, 2 kg, 0 kg and 1 kg per unit. Supply of other types of material consumed is unlimited. Machine hours
available are 500 hours and requirements are 8, 5, 0 and 4 hours for A, B, C and D each per unit. Labour
hours are limited to 900 hours and requirements are 3, 2, 1 and 5 hours for A, B, C and 0 respectively.
MASTER MINDS

How should a firm approach so as to maximize it profitability? Formulate this as Linear Programming
Problem. You are not required to solve the LPP. (D 07 - 8M)
Problem 25: A company manufactures items X1 and X2 which are sold at a profit of Rs 35 per unit of X1
and Rs. 25 per unit of X2. X1 requires 3 kgs. of materials, 4 man-hours and 2 machine hours per unit. X2
requires 2 kgs. of materials, 3 man-hours and 2 machine-hours per unit. During each production run, there
are 350 kgs, of materials available, 600 man-hours and 550 machine-hours for use. (J 09 - 2M)
Formulate under Simplex method of linear programming:
• the objective function and the linear constraints, and
• the equations after introducing slack variables.
• What are the various methods of solving a linear Programming .Problem?
Problem 26: A small manufacturing firm produces two types of gadget A and B, which are first processed
in the foundry, then sent to the machine for finishing. The number of man-hours of labour required in each
shop for the production of each unit of A and B and the number of man-hours the firm has available per
week are as follows: (D 11 - 3M)
Foundry Machine Shop
Product A: Man-hours/ unit 10 5
Product B: Man-hours/unit 6 4
Firm’s capacity per week (in hours) 1000 600
Construct the objective function and the corresponding equations for calculating how many units should
be produced per week so that the profit is maximum. The Profit on the sale of A is Rs 30 per unit as
compared to B’s Rs 20 per unit.
Problem 27 The annual hand made furniture show and sales occurs next month and the school of
vocational studies is playing to make furniture for the sale. There are three wood working classes -1 year,
II year, III year at the school and they have decided to make three styles of chairs A, B and C. Each chair
must receive work in each class and the time in hours for each chair in each class is given. (ICWA - M)
Chair I year II year III year
A 2 4 3
B 3 3 2
C 2 1 4
In the next month there will be 120 available in I year class, 160 in the second year class and 100 hours in
third year class to produce chairs. The teacher of the wood working class feels that a maximum of 40
chairs can be sold at the show. The teacher has determined that
The profit from each type of chair will be A - Rs.40, B - Rs.35 and C - Rs.30. Formulate a linear
programming model to determine how many chairs should be produced to maximise profit.
FILL IN THE BLANKS
1. ____ analysis reflects a general a general
theory of production based on the idea of
economic interdependence (Input-output)
2. ___ is a mathematical technique for allotting
limited resources in an optimal manner.
(Linear programming)
3. A ____ represents costless process whose
function is to ‘use up otherwise unemployed
capacity, say, machine hour or otherwise
capacity. (Slack variable)
4. The _______ variables are fictions and do
not have any physical meaning (Artificial)
5. ___ applications are late to a LPP where
goods are to be transported from “m”
production locations to “n” sale locations
(warehouses). (Transportation)

6. ____ linear programming helps in finding
optimum (Production mix determination)
7. In solving linear programming problem
______ method is generally used where
there are two or three variables
(Graphic), (J 10 - 1M)
8. The_____ Consists of a powerful desktop
computer and graphics software that enables
a designer to manipulate geometric shapes
(CAD) (J 10 - 1M)
9. Under input-output analysis only_____ input
is treated as scarce. (labour)
10. Optimum Capacity is rate of output at which
there is __ to change the size of the plant.
(no incentive)
11. PERT is used in ____ jobs. (non-repetitive)
12. _____ uses algebraic procedure to solve any
question which satisfies the test of linearity
and certainty (Simplex Method)
13. _____ is the most Powerful and popular
method for solving linear Programming
programs. (Simplex Method)
14. __ is used to know the minimum cost of
transportation of a Product from various
origins to different distribution and
consumption centres
(Transportation Method)
15. A___ is a reprogrammable, multifunctional
manipulator designed to move materials,
parts, tools(or) specialized devices through
variable Programmed motions for the
Performance of a variety of tasks (robot)
16. When the machine are programmed through
their own minicomputers and have memories
to store these programs, they are Called____
Machines. (Computer numerical Control)
17. _________ is a Planning technique that
permits some objective functions to be
minimized (or) maximized with in the frame
work of given situational restrictions
(Linear Programming)
18. ____ variable are fictitious and do not have
any physical meaning. (Artificial variables)
MULTIPLE CHOICE QUESTIONS
1. Application of technology or process to the
raw material to add use value is known as:
a) Product b) Production
c) Application of technology
d) Combination of technology and process
2. Technological development is an:
a) Upward trend b) Downward trend
c) Seasonal trend d) Erratic trend
3. Linear Programming is a technique used in
a) Plant layout (Dec 10 - 1M)
b) Production Programme
c) Product mix
d) Manufacturing sequence.
4. The act of assessing the future and making
provisions for it is known as: (J 10, 09 - 1M)
a) Planning b) Forecasting
c) Assessment d) Scheduling
5. JIT standard (J 10 - 1M)
a) Just in time Purchase;
b) Just in time Production
c) Just in time use of Materials
d) Just in time order of materials
6. Addition of value to raw materials through
application of technology is
c) Advancement d) Transformation
7. The incentive plan takes into account ratio of
labour costs to production value:
a) Rowan plan b) Gantt plan
c) Halsey plan d) Scanlon plan
8. Z chart is used for :
a) Cost control b) Quality control
c) Programme control d) Job control
9. FMS is
a) Future Manufacturing System
b) Flexible Manufacturing System
c) Forwarded Manufacturing System
d) Favorable Manufacturing System
10. Application of technology or process to the
raw material to add use value is known as:
c) Application of technology
d) Combination of technology and process.
11. In Production by disintegration the material
undergoes:
a) Change in economic value only
b) Change in physical and chemical
characteristics
c) Change in technology only
MASTER MINDS

d) None of the above
12. Use of any process or procedure designed to
transform a set of input elements into a set of
output elements is known as:
a) Transformation process
b) Transformation of input to output
c) Production d) Technology change.
13. Conversion of inputs into outputs is known
as:
a) Application of technology
b) Operations management
c) Manufacturing products
d) Product.
14. The desired objective of Production and
Operations Management is:
a) Use cheap machinery to produce
b) To train unskilled workers to manufacture
goods Perfectly
c) Optimal utilization of available resources
d) To earn good profits.
15. Manufacturing system often produces:
a) Standardized products
b) Standardized products in large volumes
c) Substandard products in large volumes
d) Products and services in limited volume.
16. Most important benefit to the consumer from
efficient production system is
a) He can save money
b) He will have product of his choice easily
available
c) He gets increased use value in the product
d) He can get the product on credit.
17. A method in which a trend line drawn in such
a way that the sum of the squares of
deviations of. the actual points above and
below the trend line is at the minimum is
known as:
a) Squared trend method
b) Equal square method
c) Adjusted square method
d) Least Square method.
ABBREVIATIONS
1. CAD - Computer-Aided Design
2. NC - Numerical Control
3. CNC - Computer Numerical Control
(J 08 - 1M)
4. AIS - Automated Identification
5. ASRS - Automated Storage and Retrieval
System (J 11, D 08 - 1M)
6. AGV - Automated guided Vehicles
(D 08 - 1M)
7. FMS - Flexible Manufacturing Systems
8. CIM - Computer Integrated Manufacturing.
` (D 10 - 1M)
9. MTM - Method Time Measurement
10. MBO - Management by Objective.(D 11 -
1M)
11. RA - Relaxation Allowance
12. PERT - Programme Evaluation and
Review Technique.
13. FMS - Flexible Manufacturing System
14. JIT - Just In Time
15. VAT - Value Added Tax
16. CRAF - Computerized Relative Allocation
of Facilities Techniques
17. BPE - Business Process Engineering
18. IBFS - Initial Basic Feasible Solution
19. VAM - Vogel’s Approximation Method
(J 11 - 1M)
20. CAM - Computer Aided Manufacture
21. DNC - Direct numerically Controlled machine
22. TCM - Total Cost Management
(D 11 - 1M)
23. ABFS - Alternative Basic Feasible
Solution (D 11 - 1M)
24. EMQ - Economic Manufacturing
Quantity
TRUE / FALSE STATEMENTS
1. FMS Stands for Flexible Machine System
(False) (J 11 - 1M)
2. Industrial trucks are used to pick up and
move materials in different routes. (False)
3. Linear Programming can solve question
involving variables not capable of being
expressed in quantitative terms. (False)
4. Total output of all sectors is equal to total
input of all sectors. (True)
5. A slack variable represents unused capacity.
(True)

6. Allowances for non-availability of materials
power failure and breakdown of machines
are provided for in the standard time for an
operation/job. (False)
7. Technology life cycle has five stages
(False)
8. Technological Change is a major factor in
gaining Competitive advantage. (True)
9. Linear Programming is a mathematical
technique for allotting limited resources in an
optimum manner. (True)
10. Input- output analysis is also known as
analysis of inter- industry (or) inter-Sector
flows (or) deliveries (or) analysis of inter –
industry relations. (True)
11. The Main Purpose of introducing slack variable
in the Simplex Method of Linear Programming is
to convert the inequalities into equalities. (True)
ANSWERS FOR MCQ’s
1. B 2. A 3. C 4. B 5. B
6. B 7. D 8. C 9. B 10. B
11. B 12. C 13. B 14. C 15. A
16. C 17. D 18. 19. 20.
MATCHING
1. Match the terms shown in Table A with relevant terms in Table B.
Table A Table B
1.
ALDEP
a. Transportation application
2.
MRP
b. Quality control
3.
CPM
c. Demand for a product or service has to be justified each time budget is
prepared.
4.
VAM
d. Inventory management.
5.
AOQ
e. Cost control
6.
EDD
f. Plant layout
7.
ZBB
g. Work measurement technique
8.
VA
h. Project planning
9.
BMT
i. Japanese technology
10.
BPR
j. Job sequencing
11.
USP
k. Standardisation
12.
ISO
l. Machine tool
13.
CNC
m. Project funding
MASTER MINDS

14.
IFCI
n. Marketing strategy
15.
JIT
o. Its essence lies in two questions – Why and What if cutting across all functions.
Ans: (1, f), (2, d), (3, h), (4, a), (5, b), (6, j), (7, c), (8, e), (9, g), (10, o), (11, n), (12, k), (13, l), (14, m), (15, i)
2. Expand the terms in List 'A' and match them with the related functional areas of production
management in List 'B'.
List'A' List 'B'
1. SPT - Shortest Processing Time a. Production control
2. ISO - International Standards Organisation b. Work measurement
3. CNC - Computer Numerical Control c. Scheduling
4. MTM - Methods Time Measurement d. Machine tool
5. WIP - Work-in-process e. Standardisation
Ans: (1, c), (2, e), (3, d), (4, b), (5, a)
3. Given below are two lists - list 'A' containing six observations and list 'B' containing various functional
areas associated with production management.
Expand the abbreviations and match them with the corresponding functional area.
List‘A' List 'B'
1. LP - Linear Programming a. Quality control
2. PERT - Programme Evaluation and
Review Technique
b. Project planning
3. CRAFT - Computerised Relative
Allocation of Facilities Technique
c. Inventory management
4. MRP - Materials Requirement Planning d. Product design
5. CAD - Computer Aided Design e. Product mix
determination
6. AOQ - Average Outgoing Quality f. Plant layout
Ans: (1, e), (2, b), (3, f), (4, c), (5, d), (6, a)
4. Match the terms shown in List A with relevant terms List B
List A List B
1. LP - Linear Programming a. Product design
2. PERT - Programme Evaluation and Review Technique b. Quality control
3. MTM - Methods Time Measurement c. Project funding
4. VA - Value Analysis d. Project viability checking
5. CRAFT - Computerized Relative Allocation of Facilities
Techniques
e. Inventory management
6. MRP - Materials Requirement Planning f. Cost control
7. CBA - Cost Benefits Analysis g. Product-mix determination
8. CAD - Computer Aided (or Assisted) Design h. Plant layout
9. IFCI - Industrial Finance Corporation of India i. Project Planning
10. AOQ - Average outgoing Quality j. Work measurement
Ans: (1, g), (2, i), (3, j), (4, f), (5, h), (6, e), (7, d), (8, a), (9, c), (10, b)

5. Expand the following 10 abbreviations indicated in column X and then match the same with the most
appropriate one indicated in Column Y on the right-hand side.
X Y
1. SPT - Shortest Processing Time a. Standardization
2. ICICI - Industrial Credit and investment
Corporation of India
b. Labour related standards
3. ABC - Always Better Control c. Scheduling
4. ISO - International Standards Organization d. Tax based on cost of additional Processing
5. PPC - Production Planning and Control e. Venture Capital
6. LCL - Lower Control Limit f. Machine used for producing a class of
Products
7. SPM - Special Purpose Machine Tools g. Manufacturing Planning and monitoring
8. VAT - Value Added Tax h. Marketing strategy
9. USP - Unique Selling Proposition i. Statistical Quality Control
10. ILO - International Labour Organization j. Classification based on annual usage value
Ans: (1, c), (2, e), (3, j), (4, a), (5, g), (6, i), (7, f), (8, d), (9, h), (10, b)
THE END
MASTER MINDS

Input-output Ratio & Technology Life-Cycle

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