L21-w10 - Outline SILICON CHIP CORPORATION Range Analysis...

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Outline SILICON CHIP CORPORATION Range Analysis for Objective Coefficients Resource Variations, Marginal Values, and Ran Math 407A: Linear Optimization Lecture 20 Math Dept, University of Washington March 5, 2010 Lecture 20: Math 407A: Linear Optimization Math Dept, University of Washington
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Outline SILICON CHIP CORPORATION Range Analysis for Objective Coefficients Resource Variations, Marginal Values, and Ran SILICON CHIP CORPORATION Range Analysis for Objective Coefficients Resource Variations, Marginal Values, and Range Analysis Pricing Out Lecture 20: Math 407A: Linear Optimization Math Dept, University of Washington
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Outline SILICON CHIP CORPORATION Range Analysis for Objective Coefficients Resource Variations, Marginal Values, and Ran SILICON CHIP CORPORATION A Silicon Valley firm specializes in making four types of silicon chips for personal computers. Each chip must go through four stages of processing before completion. First the basic silicon wafers are manufactured, second the wafers are laser etched with a micro circuit, next the circuit is laminated onto the chip, and finally the chip is tested and packaged for shipping. The production manager desires to maximize profits during the next month. During the next 30 days she has enough raw material to produce 4000 silicon wafers. Moreover, she has 600 hours of etching time, 900 hours of lamination time, and 700 hours of testing time. Taking into account depreciated capital investment, maintenance costs, and the cost of labor, each raw silicon wafer is worth $1, each hour of etching time costs $40, each hour of lamination time costs $60, and each hour of inspection time costs $10. The production manager has formulated her problem as a profit maximization Lecture 20: Math 407A: Linear Optimization Math Dept, University of Washington
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Outline SILICON CHIP CORPORATION Range Analysis for Objective Coefficients Resource Variations, Marginal Values, and Ran SILICON CHIP CORPORATION Initial Tableau x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 b raw wafers 100 100 100 100 1 0 0 0 4000 etching 10 10 20 20 0 1 0 0 600 lamination 20 20 30 20 0 0 1 0 900 testing 20 10 30 30 0 0 0 1 700 2000 3000 5000 4000 0 0 0 0 0 Opt. Tableau x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 b 0 . 5 1 0 0 . 015 0 0 - . 05 25 - 5 0 0 0 - . 05 1 0 - . 5 50 0 0 1 0 - . 02 0 . 1 0 10 0 . 5 0 0 1 . 015 0 - . 1 . 05 5 - 1500 0 0 0 - 5 0 - 100 - 50 - 145 , 000 Lecture 20: Math 407A: Linear Optimization Math Dept, University of Washington
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Outline SILICON CHIP CORPORATION Range Analysis for Objective Coefficients Resource Variations, Marginal Values, and Ran Range Analysis for Objective Coefficients Range analysis is a tool for understanding the effects of both objective coefficient variations as well as resource availability variations. Lecture 20: Math 407A: Linear Optimization Math Dept, University of Washington
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Outline SILICON CHIP CORPORATION Range Analysis for Objective Coefficients Resource Variations, Marginal Values, and Ran Range Analysis for Objective Coefficients Range analysis is a tool for understanding the effects of both objective coefficient variations as well as resource availability variations.
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