1. LINEAR PROGRAMMING (LP)
Lecture 08
Dr. Arshad Zaheer

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

3. 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

9. 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.

15. 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.

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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