Sources: Visual - various maths sites (credits to original creator) Questions - Dong Zong's Textbook

1. 𝒑𝒈 𝟏𝟎𝟑 − 𝟏𝟎𝟒
≥ 29
We are looking for integer values of x and y in the feasible region
where z has the greatest value.
We could substitute all the possible (x , y) values in the feasible
region into z to get the largest value but that would be too long
and tedious.
linear objective function
① Determine the gradient for the line
representing the solution
② Construct parallel lines within the
feasible region to find the solution

2. 𝒑𝒈 𝟏𝟎𝟗 linear objective function
𝑅

3. 𝒑𝒈 𝟏𝟎𝟗 linear objective function
𝑅

4. 𝒑𝒈 𝟏𝟏𝟎 linear objective function
𝑅

5. 𝒑𝒈 𝟏𝟏𝟎 linear objective function
𝑅

6. 𝒑𝒈 𝟏𝟎𝟒 − 𝟏𝟎𝟔 linear objective function

7. 𝒑𝒈 𝟏𝟏𝟏 linear objective function

8. When feeding buckwheat species, need to supply at
least 11 units, 13 units, 15 units of the 3 nutrients each
day.
There are 2 kinds of feed, A and B.
Price per kg for A = 300 yuan.
Price per kg for B = 400 yuan.
The unit quantity of each nutrien contained in each kg of
A and B is shown in the table below. Min feeding cost = ?
𝒑𝒈 𝟏𝟏𝟏 linear objective function
300
400
𝑦𝑢𝑎𝑛
11 13 15
𝑚𝑖𝑛
𝑥
𝑦
𝑥 + 2𝑦 ≥ 11
3𝑥 + 𝑦 ≥ 13
2𝑥 + 2𝑦 ≥ 15
𝑥 ≥ 0
𝑦 ≥ 0
𝑅
𝑧 = 300𝑥 + 400𝑦
𝑧𝑚𝑖𝑛 = 300(4) + 400(3.5)
= 2,600 𝑦𝑢𝑎𝑛

9. 𝒑𝒈 𝟏𝟎𝟔 − 𝟏𝟎𝟕 linear objective function

10. 𝒑𝒈 𝟏𝟏𝟏 linear objective function

11. 𝒑𝒈 𝟏𝟎𝟕 − 𝟏𝟎𝟖 linear objective function

12. 𝒑𝒈 𝟏𝟎𝟗 linear objective function

13. 𝒑𝒈 𝟏𝟎𝟗 linear objective function
A transportation company can load good for 2 factories,
A and B.
Factory A box = 2 * 40 kg charge per box = 2.20 yuan
Factory B box = 3 * 50 kg charge per box = 3.00 yuan
Truck max weight = 37,000 kg
Truck max volume = 2,000 boxes
Max charge = ?
A B max
Weight 40 50 37,000
Volume (box) 2 3 2,000
Charge per box
(yuan)
2.20 3.00 ?
4𝑥 + 5𝑦 ≤ 3,700
2𝑥 + 3𝑦 ≤ 2,000
𝑥 ≥ 0
𝑦 ≥ 0
𝑅
𝑧 = 2.20𝑥 + 3𝑦
𝑧𝑚𝑎𝑥 = 2.20(550) + 3(300)
= 2,110 𝑦𝑢𝑎𝑛
𝑠𝑖𝑚𝑝𝑙𝑖𝑓𝑦 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛

14. 𝒑𝒈 𝟏𝟎𝟗 − 𝟏𝟏𝟏 linear objective function

15. 𝒑𝒈 𝟏𝟎𝟗 − 𝟏𝟏𝟏 linear objective function