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Linear programming

# Linear programming - Intro to Linear Programming Comm 354...

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November 16, 2009; Intro to Linear Programming Comm 354 Simple Problem Suppose you have two products: Z1 Z2 Selling Price \$18 \$23 Variable Costs \$14 \$20 Fixed Costs \$2 \$1 Profit \$2 \$2 Labor Minutes 2 1 Machine minutes 3 4 Demand 400 500 Labor minutes capacity 1,000 Machine minutes capacity 2,400 How do we optimize the profit?

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Solution: Answer: The solution involves choosing Z1 and Z2 to maximize the following linear program: Max 4 Z1 + 3Z2 Subject to: 2Z1 + Z2 <= 1000 (Resource Constraint) 3Z1 + 4Z2 <= 2400 (Resource Constraint) Z1 <= 400 Z2 <= 500 (Demand Constraints) Since this is a relatively simple problem, the solution can be inferred graphically. Alternatively, one can feed the linear program into Excel using the “solver” plug-in to find that optimal sales quantities are 320 Z1’s and 360 Z2’s. We present the graphical solution in class. See the excel worksheet “simple.xls” for a template that can be modified for future LP problems. Here is the output from that spreadsheet: Microsoft Excel 11.0 Answer Report Worksheet: [simple.xls]Sheet1
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