Optimization+II E10

# Optimization+II E10 - Optimization II Optimization II Rob...

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ptimization II Optimization II Rob Leachman 10, pring, 2010 E10, Spring, 2010 Feb. 3, 2010 Feb. 3, 2010 Optimization E10 Prof. Leachman 1

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hat is Optimization What is Optimization • Calculation of how best to operate or configure a ystem system – Decision variables ( A for what we can adjust ) – Objective function ( B for what’s best ) – Constraints on variables ( C for how are we constrained ) • Mathematical methods of optimization – Calculus: Functional characterization of possible decisions and economic consequences – Search: Enumeration and evaluation of alternative decisions • Directed search (always move to a better alternative) • Proof of optimality without evaluating every alternative Feb. 3, 2010 Optimization E10 Prof. Leachman 2 py g y
troduction to Linear Introduction to Linear Programming: Example Formulations, nd Extensions and Extensions Feb. 3, 2010 Optimization E10 Prof. Leachman 3

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inear Programming Linear Programming he term “linear program” refers to an The term linear program refers to an optimization problem with an objective that is a linear function of the decision variables, subject to a set of linear constraints on the decision variables • The word “program” refers to the plan prescribed by the solution to the problem. (The original roblem for which LP was developed was to find problem for which LP was developed was to find the best program of training and assignments for S Air Force officers ) Feb. 3, 2010 Optimization E10 Prof. Leachman 4 US Air Force officers.)
tereo Retailing Stereo Retailing • Retail outlet has 400 sq ft of floor space and a budget for stocking items of \$8000 • Model X receiver has wholesale cost of \$100, ells for \$150 and requires 2 sq ft of display sells for \$150, and requires 2 sq ft of display space • Model Y set of speakers has wholesale cost of \$50, sells for \$70, and requires 4 sq ft of display space • Demand for receivers is expected to be at most 60 units Feb. 3, 2010 Optimization E10 Prof. Leachman 5

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tereo Retailing (cont.) Stereo Retailing (cont.) A: Let x = number of receivers to stock = number of sets of speakers to stock y = number of sets of speakers to stock : aximize 50x + 20y ross profit B: Maximize 50x + 20y gross profit C: Subject to 2x + 4y 400 floor space 100x + 50y 8000 budget x 60 sales limit x, y 0 Feb. 3, 2010 Optimization E10 Prof. Leachman 6 x, y integer
Diet (Blending Problem) • The hospital wants to concoct a desert shake eeting certain dietary restrictions meeting certain dietary restrictions • Ingredients: Egg custard, Ice cream, Butterscotch syrup Egg Ice Butterscotch Requirement Custard Cream Syrup holesterol 0 50 0 = 175 Cholesterol 50 150 90 <= 175 Fat 0 100 50 <= 150 Protein 70 10 0 >= 200 Calories 30 80 200 >= 100 Cost per oz. 0.15 0.25 0.10 Feb. 3, 2010 Optimization E10 Prof. Leachman 7

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Diet (Blending) Problem (cont.) Let E = ounces of egg custard base in the shake C = ounces of ice cream in the shake S = ounces of butterscotch syrup in the shake Minimize cost 015 025 010 ... EC S Subject to cholesterol t 50 150 90 175 E CS 00 0 fat protein calories 100 C S 70 10 E C 200 30 80 E Feb. 3, 2010 Optimization E10 Prof. Leachman 8 EC S ,, 0
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Optimization+II E10 - Optimization II Optimization II Rob...

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