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Lecture 08 Dr. Arshad Zaheer LINEAR PROGRAMMING (LP)

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Recap Linear Programming Requirements of a Linear Programming Problem Maximization Problems Minimization Problems Linear Programming Methods Graphical Method Simplex Method (will do later)

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Formulating Linear Programming Problems Shader Electronics Example Graphical Solution to a Linear Programming Problem Graphical Representation of Constraints Iso-Profit Line Solution Method Corner-Point Solution Method

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Product AProduct B Machine minutes per Unit Machine minutes per unit Machine W26 Machine X84 A manufacturing department produces two products A & B. Both products are produced on the same automatic machines, the time taken on each machine varies as: Total machine minutes available are as under: Machine W = 66 Machine X = 120 The expected profit on product A and B is Rs. 16 and Rs. 12 respectively. Calculate the number of units of product A and B, the department should produce to maximize profit.

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Product AProduct B Machine minutes per Unit Machine minutes per unit Machine W26 Machine X84 Machine Y48 A manufacturing department produces two products A & B. Both products are produced on the same automatic machines, the time taken on each machine varies as: Total machine minutes available are as under: Machine W = 66 Machine X = 120 Machine Y = 96 The expected profit on product A and B is Rs. 16 and Rs. 12 respectively. Calculate the number of units of product A and B, the department should produce to maximize profit.

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To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7-22© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Flair Furniture Company Data - Table 7.1 Hours Required to Produce One Unit Department T Tables C Chairs Available Hours This Week Carpentry Painting &Varnishing 4242 3131 240 100 Profit Amount $7 $5 Constraints: 4T + 3C 240 (Carpentry) 2T + 1C 100 (Paint & Varnishing) Objective: Max: 7T + 5C

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To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7-23 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Flair Furniture Company Constraints Number of Tables 120 100 80 60 40 20 0 Number of Chairs 20 40 60 80 100 Painting/Varnishing Carpentry

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To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7-24 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Flair Furniture Company Feasible Region 120 100 80 60 40 20 0 Number of Chairs 20 40 60 80 100 Number of Tables Painting/Varnishing Carpentry Feasible Region

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To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7-25© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Flair Furniture Company Isoprofit Lines Number of Tables Number of Chairs 120 100 80 60 40 20 0 20 40 60 80 100 Painting/Varnishing Carpentry 7T + 5C = 210 7T + 5C = 420

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To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7-26© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Flair Furniture Company Optimal Solution Number of Chairs 120 100 80 60 40 20 0 20 40 60 80 100 Number of Tables Painting/Varnishing Carpentry Solution (T = 30, C = 40) Isoprofit Lines

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To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7-27© 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Flair Furniture Company Optimal Solution Number of Chairs 120 100 80 60 40 20 0 20 40 60 80 100 Number of Tables Painting/Varnishing Carpentry Solution (T = 30, C = 40) Corner Points 1 2 3 4

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