Quantitative Techniques for Managerial Decisions Khanna

Introduction to Operations Research: A Computer-oriented Algorithmic Approach By Billy E. Gillett

Assignment - Linear Programming

Q.1 Maximize f = 5x1 – 4x2 + 6x3 + 8x4

st. x1 + 7x2 + 3x3 + 7x4 < 46

3x1 – x2 + x3 + 2x4 < 8

2x1 + 3x2 - x3 + x4 < 10

X1 > 0, x2 > 0, x3 > 0, x4 > 0

Q.2 Minimize f = 2x1 + 3x2 + x3

st. x1 + 4x2 + 2x3 > 8

3x1 + 2x2 > 6

X1 > 0, x2 > 0, x3 > 0

Q.3 A company wants to purchase at most 1800 units of a product. There are two

types of the product, M1 and M2 available.

M1 occupies 2ft3, costs Rs 4.0 and the company makes a profit of Rs. 3.0. M2

occupies 3ft3, cost Rs. 5.00 and the company makes a profit of Rs. 4.00. If the

budget is Rs. 5500/- and warehouse has explicitly 3000 ft3 for the product,

a) Formulate the problem as linear programming problem

b) Solve the problem by simplex method.

Q.4 A manufacturing firm has discontinued production of a certain unprofitable product

line. This created considerable excess production capacity. Management is

considering devoting this excess capacity to one or more of three products; call

them products 1, 2, 3. The available capacity on the machine that might limit

output is summarized in the following table:-

Machine type Available time (machine hour per week)

Milling machine 500

Lathe 350

Grinder 150

The number of machine hours required for each unit of the respective products is:

Machine type Product 1 Product 2 Product 3

Milling machine 9 3 5

Lathe 5 4 4

Grinder 3 0 2

The unit profit would be Rs. 30.00, Rs 12.00 and Rs. 19.00 respectively, on

product 1, 2, and 3.

a) Formulate the Linear programming model for determining how much

of each product the firm should produce to maximize profit.

b) Solve the problem by the simplex method.

Q.5 Minimize f = 5x1 + 2x2

St. 4x1 + x2 > 8

X1 + x2 < - 5

X1, x2 > 0

a) Solve this problem by graphical method

b) Solve this problem by simplex method