A firm can produce three types of cloth, say A, B, and C. Three kinds of wool ar

Question

A firm can produce three types of cloth, say A, B, and C. Three kinds of wool are required for it, say red wool, green wool and blue wool. One unit length of type A cloth needs 2 yards of red and 3 yards of blue wool; one unit length of type B cloth needs 3 yards of red wool, 2 yards of green wool and 2 yards of blue wool and one unit length of type C cloth needs 5 yards of green wool and 4 yards of blue wool. The firm has only a stock of 8 yards of red wool, 10 yards of green wool and 15 yards of blue wool. It is assumed that the income obtained from one unit length of type A cloth is Rs 3.00, of type B cloth is Rs 5.00 and that of type C is Rs 4.00.
Formulate the problem as a LINEAR PROGRAMMING PROBLEM to maximise the total income from the finished cloth.

Explanation / Answer

The question ask only to formulate the problem and not solve it. So I will only provide a solution to formulate it -

Variables -

1. produce A type of cloth in yard = A

2. produce B type of cloth in yard = B

1. produce C type of cloth in yard = C

Constraints -

1. A, B and C are non-negative integers

2. Maximum 8 yard of red wool can be used, so : 2A+3B <= 8

3. Maximum 10 yard of green wool can be used, so : 2B + 5C <= 10

4. Maximum 15 yard of blue wool can be used, so : 3A+2B + 4C <= 15

Objective -

maximize the income = 3A + 5B + 4C

please please upvote the answer.

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