lecture 08 dr. arshad zaheer linear programming (lp)
TRANSCRIPT
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Lecture 08
Dr. Arshad Zaheer
LINEAR PROGRAMMING (LP)
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RecapRecap
Linear ProgrammingLinear Programming
Requirements of a Linear Programming Requirements of a Linear Programming ProblemProblem
Maximization ProblemsMaximization Problems
Minimization ProblemsMinimization Problems
Linear Programming MethodsLinear Programming Methods
Graphical MethodGraphical Method
Simplex Method (will do later)Simplex Method (will do later)
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Formulating Linear Programming Formulating Linear Programming ProblemsProblems Shader Electronics ExampleShader Electronics Example
Graphical Solution to a Linear Graphical Solution to a Linear Programming ProblemProgramming Problem Graphical Representation of ConstraintsGraphical Representation of Constraints
Iso-Profit Line Solution MethodIso-Profit Line Solution Method
Corner-Point Solution MethodCorner-Point Solution Method
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Product A Product B
Machine minutes
per Unit
Machine minutes
per unit
Machine W 2 6
Machine X 8 4
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 = 66Machine X = 120The 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 A Product B
Machine minutes
per Unit
Machine minutes
per unit
Machine W 2 6
Machine X 8 4
Machine Y 4 8
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 = 66Machine X = 120Machine Y = 96The 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 7.1Hours Required to Produce One Unit
DepartmentT
TablesC
Chairs
AvailableHours This
Week
CarpentryPainting &Varnishing
42
31
240100
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
Num
ber
of C
hair
s
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
Num
ber
of C
hair
s
20 40 60 80 100Number of Tables
Painting/Varnishing
CarpentryFeasibleRegion
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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
Num
ber
of C
hair
s120
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
Num
ber
of C
hair
s
120
100
80
60
40
20
0
20 40 60 80 100Number of Tables
Painting/Varnishing
Carpentry
Solution(T = 30, C = 40)
Isoprofit LinesIsoprofit 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
Num
ber
of C
hair
s
120
100
80
60
40
20
0
20 40 60 80 100Number of Tables
Painting/Varnishing
Carpentry
Solution(T = 30, C = 40)
Corner PointsCorner Points
1
2
3
4