Post on 16-Dec-2015
transcript
Lecture 08
Dr. Arshad Zaheer
LINEAR PROGRAMMING (LP)
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)
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
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.
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.
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
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
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
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
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
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