Homework 2

# Homework 2 - University of California Davis Department of...

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Department of Agricultural and Resource Economics “We are what we repeatedly do. Excellence then is not an act, but a habit.” Aristotle Copyright c ± 2011 by Quirino Paris. ARE 155 Winter 2011 Prof. Quirino Paris HOMEWORK #2 Due Tuesday, January 18 1. Given the following LP problem max Z = 6 x 1 + 3 x 2 subject to 2 x 1 + 6 x 2 12 5 x 1 + 2 x 2 10 x 1 and x 2 0 a) Graph the output space. b) Graph the input requirement space (do not forget vectors associated with slack variables). c) For each extreme point (basic feasible solution) in the output space indicate the corresponding basis in the input requirement space. d) Solve the problem by graphical methods and report the optimal basis and the optimal solution. (In a graph, it may be diﬃcult to read the exact optimal solution. Be as accurate as possible: choose the appropriate measurement units on the axes of your diagram.) 2. Given the following LP problem max TR = 2 x 1 + 4 x 2 + 6 x 3 subject to 3 x 1 + x 2 4 x 3 9 x 1 + 4 x 2 + 3 x 3 8 x i 0 , i = 1 , 2 , 3 a) graph the set of constraints in the input requirement space and indicate ex- plicitly all the feasible bases. b) for each feasible basis in a) write down the corresponding basic feasible solution in qualitative terms . c) Use the notion of a total cost function to derive marginal cost. Derive marginal

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Homework 2 - University of California Davis Department of...

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