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# hw4 - Homework 4 Due Exercise 3 page 111 Solve Problem 5(a...

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Homework 4 Due: February 17, 2009 Exercise 3, page 111 Solve Problem 5 (a) of Set 3.4A (page 107) by the two-phase method. Exercise 1, page 118 For the following LP, identify three alternative optimal basic solutions, and then write a general expression for all the nonbasic alternative optima comprising these three basis solutions: maximize z = x 1 + 2 x 2 + 3 x 3 subject to x 1 + 2 x 2 + 3 x 3 10 x 1 + x 2 5 x 1 1 x 1 , x 2 , x 3 0 . Note: Although the problem has more than three alternative basic solution optima, you are only required to identify three of them. Exercise 2, page 120 : Consider the LP: maximize z = 20 x 1 + 10 x 2 + x 3 subject to 3 x 1 - 3 x 2 + 5 x 3 50 x 1 + x 3 10 x 1 - x 2 + 4 x 3 20 x 1 , x 2 , x 3 0 . (a) By inspecting the constraints, determine the direction ( x 1 , x 2 , or x 3 ) in which the solution space is unbounded. (b) Without further computations, what can you conclude regarding the optimum objective value? 1

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Exercise 1, Page 134 : In the TOYCO model, suppose that the changes D 1 , D 2 , and D 3 are made simulta- neously in the three operations.
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