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**LINEAR PROGRAMMING (LP)**

Lecture 08 Dr. Arshad Zaheer

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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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**Total machine minutes available are as under: Machine W = 66 **

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: Product A Product B Machine minutes per Unit Machine minutes per unit Machine W 2 6 Machine X 8 4 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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**Total machine minutes available are as under: Machine W = 66 **

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: Product A Product B Machine minutes per Unit Machine minutes per unit Machine W 2 6 Machine X 8 4 Machine Y 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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**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 4 2 3 1 240 100 Profit Amount $ $5 Constraints: 4T + 3C 240 (Carpentry) 2T + 1C 100 (Paint & Varnishing) Objective: Max: 7T + 5C 7-22 To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna

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**Flair Furniture Company Constraints**

120 100 80 60 40 20 Number of Chairs Painting/Varnishing Carpentry Number of Tables To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7-23

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**Flair Furniture Company Feasible Region**

120 100 80 60 40 20 Number of Chairs Number of Tables Painting/Varnishing Carpentry Feasible Region To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7-24

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**Flair Furniture Company Isoprofit Lines**

Number of Tables Number of Chairs 120 100 80 60 40 20 Painting/Varnishing Carpentry 7T + 5C = 210 7T + 5C = 420 To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7-25

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**Flair Furniture Company Optimal Solution**

Number of Chairs 120 100 80 60 40 20 Number of Tables Painting/Varnishing Carpentry Solution (T = 30, C = 40) Isoprofit Lines To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7-26

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**Flair Furniture Company Optimal Solution**

Number of Chairs 120 100 80 60 40 20 Number of Tables Painting/Varnishing Carpentry Solution (T = 30, C = 40) Corner Points 1 2 3 4 To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 7-27

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