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