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Exam 2 Solutions

# Exam 2 Solutions - 1 CSA 273 60 Points Second Exam...

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1 CSA 273 Second Exam Solutions 60 Points March 12, 2008 1. You may use an 8 1/2 by 11 sheet (both sides) of notes and a calculator. 2. Show all work to receive full credit. If you need extra working space, use the back of the pages. 3. Definitions of decision variables and required explanations should be clear and unambiguous to a layperson. 4. Tests will be graded by next Friday. (15) Problem #1 For the following linear programming problem: Maximize 2x 1 + 3x 2 Such that x 1 + 2x 2 6 x 1 ,x 2 0 (a) On the workspace below, graph the region that satisfies the constraints.

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2 Problem #1 0 1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 12 x1 x2 Graph x 1 +2x 2 =6 5x 1 + 3x 2 = 15
3 Problem #1 (cont) Maximize 2x 1 + 3x 2 Such that x 1 + 2x 2 6 5x 1 + 3x 2 15 x 1 ,x 2 0 (b) Find the optimal solution and the value of the objective function at the optimal solution. The lines corresponding to the binding constraints: x 1 + 2x 2 = 6 5x 1 + 3x 2 =15 The optimal solution is x 1 = 12/7 and x 2 = 15/7 maximium value of the objective function = 2(12/7) + 3(15/7) = 69/7 Problem #2 In parts (a)-(c), classify each linear program as involving one of the following: 1. infeasibility 2. unboundedness 3. none of the above Put your choice in the space provided. Each of these will be worth two points with partial credit (one point) if work is shown.

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