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# hw03a_2008 - UNC-Wilmington Department of Economics and...

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UNC-Wilmington ECN 321 Department of Economics and Finance Dr. Chris Dumas Homework 3 Solutions 1) This problem shows that a change in the objective function alone can change the solution to a problem. This problem provides an example of doing a sensitivity analysis to the parameters in the objective function —we change the value of one of the parameters in the objective function and find the effects on model results. Identify the choice variables: M = number of mixed drinks per customer B = number of beers per customer Set up the optimization problem: max U = 4M + 1B M,B Subject to: M ≥ 0 Constraints re-written B ≥ 0 in “graphing form:” 3M + 2B ≤ 10 M = 3.33 – (2/3)B 3M + 1B ≤ 6 M = 2 – (1/3)B Graph the constraints: Finding the coordinates of this Extreme Point. 3.33 – (2/3)B = 2 – (1/3)B 1.33 = (1/3)B B = 4 M = 2 – 1/3 4 = 2/3 Feasible Region The Feasible Region is convex; hence, the optimal feasible solution will occur at an extreme point. Construct table of extreme points: B M U = 4M + 1B 0 0 0 0 2 8 4 2/3 6 2/3 5 0 5 Identify the solution: Maximum of U = 8 B = 0, M = 2) is the solution. When the customer’s preference for beer decreased , the customer's objective function changed. As a result, the solution to the problem changed such that the customer now buys less beer and more mixed drinks (relative to the solution of (B = 4, M = 2/3) in the original problem in the handout).

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