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Krajewski SN Supplement E - MODULE B LINEAR PROGRA MMING 1...

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Supplement E Linear Programming A. Basic Concepts 1. Linear programming is an optimization process with several characteristics a. Objective function: b. Decision variables: c. Constraints: d. Feasible region: e. Parameter: f. Certainty: g. Linearity: h. Nonnegativity: 2. Formulating a problem Example E.1 a. Step 1: b. Step 2: c. Step 3: 3. Application E.1: Problem Formulation for Crandon Manufacturing The Crandon Manufacturing Company produces two principal product lines. One is a portable circular saw, and the other is a precision table saw. Two basic operations are crucial to the output of these saws: fabrication and assembly. The maximum fabrication capacity is 4000 hours per month; each circular saw requires 2 hours, and each table saw requires 1 hour. The maximum assembly capacity is 5000 hours per month; each circular saw requires 1 hour, and each table saw requires 2 hours. The marketing department estimates that the maximum market demand next year is 3500 saws per month for both products. The average contribution to profits and overhead is $900 for each circular saw and $600 for each table saw. Management wants to determine the best product mix for the next year so as to maximize contribution to profits and overhead. Also, it is interested in the payoff of expanding capacity or increasing market share. SN:E-1
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SN:E-2 Supplement E: Linear Programming Definition of Decision Variables 1 x = 2 x = Formulation Maximize: Subject to: B. Graphic Analysis 1. What is the purpose of a graphic analysis? 2. Five basic steps a. Plot the constraints Example E.3 b. Identify the feasible region c. Plot an objective function line Corner points Example E.4 Iso-profit and iso-cost lines d. Find the visual solution e. Find the algebraic solution
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Supplement E: Linear Programming SN:E-3 Application E.2: Steps a and b for Crandon Manufacturing Plot the constraints and shade the feasible region for Crandon Manufacturing. Constraint Point 1 Point 2 x 1 x 2 x 1 x 2 1 ( , ) ( , ) 2 ( , ) ( , ) 3 ( , ) ( , )
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SN:E-4 Supplement E: Linear Programming Application E.3: Steps c and d for Crandon Manufacturing Plot one or more iso-profit lines. Let Z = $2,000,000 (arbitrary choice) Plot $900 x 1 + $600 x 2 = $2,000,000 Point 1 Point 2 Profit x 1 x 2 x 1 x 2 $2,000,000 ( , ) ( , ) Identify the visual solution.
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