4120_lecture5

# 4120_lecture5 - Computational Methods for Management and...

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Computational Methods for Management and Economics Carla Gomes Lecture 5 Reading: 3.4 and 3.5 of textbook

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Main Categories of LP problems: Resource-Allocation Problems Cost-benefit-trade-off problems Distribution-Network Problems
Dorian Auto Dorian Auto manufactures luxury cars and trucks. The company believes that its most likely customers are high-income men and women. To reach these groups, Dorian Auto has embarked on an ambitious TV advertising campaign and has decided to purchase 1- minute commercial spots on two types of programs: comedy shows and football games. Each comedy commercial is seen by 7 million high-income women and 2 million high-income men. Each football commercial is seen by 2 million high-income women and 12 million high-income men. A 1-minute comedy ad costs \$50,000, and a 1- minute football ad costs \$100,000. Dorian would like the commercials to be seen by at least 28 million high-income women and 24 million high-income men. Use LP to determine how Dorian Auto can meet its advertising requirements at minimum cost.

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Dorian Model x 1 number of 1-minute comedy ads purchased x 2 number of 1-minute football ads purchased Decision Variables Objective Function: Min z = 50 x1 + 100 x2 Constraints S.t. 7 x1 + 2 x2 >= 28; HIW 2 x1 + 12 x2 >= 24; HIM x1 >= 0; x2 >= 0;
Dorian 4 14 12 10 5 Min z = 50 x1 + 100 x2 7 x1 + 2 x2 >= 28; HIW 2 x1 + 12 x2 >= 24; HIM x1 >= 0; x2 >= 0; Z*= 50(3.6)+100(1.4)= 320 HIM HWM Optimal solution?

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Main Categories of LP problems: Resource-Allocation Problems Cost-benefit-trade-off problems Distribution-Network Problems
Resource-Allocation Problems

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Resource Allocation Problems Wyndor Glass Resources – m (plants) Activities – n (2 products) Wyndor Glass problem optimal product mix --- allocation of resources to activities i.e., choose the levels of the activities that achieve best overall measure of performance
Financial Planning Another area of application of resource-allocation problems Financial Planning Resources: Financial assets (cash, securities,accounts receivable, lines of credit, etc). Example: Capital budgeting Resources: amounts of investment capital available at different points in time.

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Think-Big Capital Budgeting Problem Think-Big Development Co. is a major investor in commercial real-estate development projects. They are considering three large construction projects
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4120_lecture5 - Computational Methods for Management and...

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