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please graph Consider the following linear programming problem Min A+ 2B s.t. A + 4B< or equal to 21 2A + B > or equal to 7 3A + 1.5B < or equal to 21 -2A + 6B > or equal to 0 A, B > or equal to 0 a. Find the optimal soulution using the graphical soulution procedure and the value of the objective function b.determine the amount of slack or surplus for each constraint (dont worry about this problem it has been emitted from the homework but if you can help me to understand this I would greatly apprecaite it) c. suppose the objective function is changed to max 5A+2B. Find the optimal solution and the value of the objective function. . Solution if you plot those inequalities in a graph . the graph should be in 1st quadrant since A,B > 0 and if you plot all the above inequlities the minimum y-intercept is 7. so the min of A+2B = 7.

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A. B. A. B. A.B.C.D. A. B. C. D. A. B. C. A. B. ( { } )A. B. A. B. C. A. B. A. B. A. B. A. B. Math 107 Final ExaminationSummer, 20151 Math 107 College AlgebraName______________________________ Final Examination: Summer, 2015Instructor __________________________ Answer Sheet Instructions: This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. Record your answers and work in this document. There are 30 problems. Problems #1-12 are multiple choice. Record your choice for each problem. Problems #13-21 are short answer. Record your answer for each problem. Problems #22-30 are short answer with work required. When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages. . Name _____________________Date___________________ MULTIPLE CHOICE. Record your answer choices. 1.7. 2.8. 3.9. 4.10. 5.11. 6.12. SHORT ANSWER. Record your answers below. 13. 14. 15. 16. 17. 18. 19. (a) (b) (c) 20. (a) (b) (c) (d) 21. (a) (b) (c) (d) SHORT ANSWER with Work Shown. Record your answers and work. Problem Number Solution 22 Answers: (a) (b) Work/for part (a) and explanation for part (b): 23 Answers: (a) (b) (c) Work for part (a): 24 Answer: Work: 25 Answer: Work: 26 Answers: (a) (b) Work for part (a) and for part (b): 27 Answer: Work: 28 Answer: Work: 29 Answers: (a) (b) Work for (b): 30 Answer: Work: College Algebra MATH 107 Summer, 2015, V3.1 Page 1 of 11 MATH 107 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Record your answers and work on the separate answer sheet provided. There are 30 problems. Problems #1–12 are Multiple Choice. Problems #13–21 are Short Answer. (Work not required to be shown) Problems #22–30 are Short Answer with work required to be shown. MULTIPLE CHOICE 1. Determine the domain and range of the piecewise functi.

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Please help me and explain 1. If all other agents choose a level of activity e, the payoff of agent i can be expressed as V(ei, e). In this case the optimization problem becomes max ei V(ei, e), Using the optimization problem, show the the conditions for coordination failures. And also discuss coordination failures with help of the game theoretical structures such as the battle of the sexes, prisoners\' dilemma and the stag hunt bu giving the real cases in the economy. Solution Problem of coordination in a shared production process. Let ej be the effort (input) of player i in the production of a public good, c. The production function is c = f(ei,e) with fi > 0 and f2> 0. Agents have identical utility functions defined over consumption and effort U(c,e), with U1 > 0, U2 < 0, and U() quasi-concave. These preferences, together with the production function, generate agent i\'s payoff function: (1) V(ei,e) = U(f(ej,e),ej. Note that V12= U1f2> 0, so the model exhibits positive spillovers. Differentiating the payoff function with respect to ei and e yields (2) V12 = U1f12 + U1lflf2 + U12f2. that preferences between consumption and effort are separable. A necessary condition for strategic complementarity is then that inputs be complementary within the production process (/12 > 0). Increases in e will induce increases in ej if /12 is large enough to offset the reduction in the marginal utility of consumption brought about by f2 > 0. If U() is linear, /12 > 0 is sufficient for strategic complementarities. Note further that - V12 UJ1/2 + Ullfl2 V1l -[U11 (fl)2 + U1f/1 + U22] The necessary condition for multiplicity (p > 1) is (4) U1(/12 + /11) + U1l[(/l)2 + /1/2] _ -U22. Multiple Equilbria are thus more likely when the utility function is not very concave with respect to consumption and effort; when inputs are highly complementary in production; and when the production function is not very concave with respect to own effort..

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