University : | UNIVERSITY OF BOTSWANA UniLearnO is not sponsored or endorsed by this college or university. |
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Subject Code : | ECO331 |
Question 1
A. After two pivot steps, the tableau of a profit maximization linear program assumes the following form:
(i) Is this an optimal tableau? Why?
(ii) What are the values of ?
(iii) Interpret the last four values of row 5.
(iv) How many choice variables would its dual program contain? Why?
B. Consider the Sequential-move capacity expansion game between Toyota and Honda. Honda moves first.
Where BL, BS and DB represent build large, build small and don’t build, respectively.
(i) Find the Nash Equilibrium of this game
(ii) Express the game above in its extensive form [5 marks] (iii) Using the Subgame-perfect Nash Equilibrium concept, find the equilibrium capacity strategy for Toyota and Honda
Question 2
A dietitian has recommended that you take a minimum of 4 units of vitamin A, 6 units of Calcium, 3 units of Protein and 1 unit of Zinc each day. Assume that your diet consists of three types of meals. Brand I costs P550 and supplies units of vitamin A, 2 units of Calcium, 4 units of Protein and 3 units of Zinc. Brand II costs P700 and supplies 4 units of vitamin A, 1 unit of Calcium, 2 units of Protein and 1 unit of Zinc. Brand III costs P200 and supplies 2 units of vitamin A, 3 units of calcium, 1 unit of Protein and 2 units of Zinc.
(i) Express the least-cost combination of nutrients that will guarantee you the daily requirements as equations and inequalities {hint: set up the LPP for this problem}
(ii) Obtain the corresponding dual to the primal in (i) above
(iii) Use the simplex method to solve the dual problem in (ii) above.
(iv) Obtain the optimal values of the primal problem in (i) from the solution of its dual in (iii) above.
B. In the beer promotion game below, two bottle stores have received a new brand of beer and each one of them can advertise it on Btv. When the advert appears on Btv, 10,000 beer drinkers will purchase the beer per week. The cost of advertising the beer is that while the one who advertises pays for the ad at Btv, the other bottle store will use its financial resources to hire more cashiers. The payoffs from this game are presented in the table below.
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