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Homework 3 - University of California Davis Department of...

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University of California, Davis 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 #3 Due Tuesday, January 25 1. Given the following primal LP problem min TC = 3 x 1 + 4 x 2 subject to 3 x 1 + 2 x 2 6 2 x 1 x 2 8 x i 0 , i = 1 , 2 a) Graph the primal problem. Write down all the extreme points and the associ- ated primal feasible bases. b) Write down the dual problem (Be careful to have all the inequalities going in the right direction before writing the dual.) c) Graph the dual problem. Write down all the extreme points of the dual problem and the associated dual feasible bases. d) Verify graphically that the basis " 2 1 1 0 # in the primal problem is not a feasible basis. 2. An investor wants to allocate her inheritance income among four construction projects and annual certificates of deposit. The outlays and cash inflows of each construction project for the first three years are as follows: Beginning of year Project First Second Third I 1 , 000 +200 +300 II 1 , 200 300 +200 III 900 100 150 IV 1 , 100 100 200 1
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(A minus sign indicates a cash outlay, while a plus sign indicates a cash inflow.) After the third year, the information about the profitability of each project is summarized in its net present value (at the beginning of the fourth year) as follows: Project I, $250; project II, $300; project III, $360; project IV, $420.
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