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HW_Solution_Chapter 03_EMSE102-202

# HW_Solution_Chapter 03_EMSE102-202 - 1 OR CHAPTER 3...

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1 OR CHAPTER 3 SOLUTIONS Section 3.2 1. max z = 30x 1 + 100x 2 s.t. x 1 + x 2 7 (Land Constraint) 4x 1 + 10x 2 40(Labor Constraint) 10x 1 30(Govt. Constraint) x 1 0, x 2 0 EF is 4x 1 + 10x 2 = 40, CD is x 1 = 3, and AB is x 1 + x 2 = 7. The feasible region is bounded by ACGH. The dotted line in graph is isoprofit line 30x 1 + 100x 2 = 120. Point G is optimal. At G the constraints 10x 1 30 and 4x 1 + 10x 2 40 are binding. Thus optimal solution has x 1 = 3, x 2 = 2.8 and z = 30(3) + 100(2.8) = 370.

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2 2. x 1 = Number of Type 1 Trucks produced daily x 2 = Number of Type 2 Trucks produced daily Expressing profit in hundreds of dollars we obtain the following formulation: max z = 3x 1 + 5x 2 s.t. x 1 /800 + x 2 /700 1 (Paint Shop Const.) x 1 /1500 + x 2 /1200 1 (Engine Shop Const.) x 1 0, x 2 0 AB is x 1 /800 + x 2 /700 = 1. CD is x 1 /1500 + x 2 /1200 = 1. Feasible region is bounded by ABE. Dotted line is z = 3x 1 + 5x 2 = 1500. Moving isoprofit line up and to right we find optimal solution to be where x 1 0 and Paint Shop constraint are binding.
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