1Medium10 marks
Give the applications of linear programming problem. A firm produces three products A, B and C. It uses two types of raw material I and II of which 5000 units and 7500 units respectively are available. The raw material requirements per unit of the products are given below :
[Raw material table]
The labour time for each unit of product A is twice that of product B and three times that of product C. The entire labour force of the firm can produce the equivalent of 3000 units of product A. The minimum demands of the three products are 600 units, 650 units and 500 units respectively. Also, the ratio of the number of units produced must be equal to 2:3:4. Assume that the profits per unit of A, B and C are ₹ 50, ₹ 50 and ₹ 80 respectively.
Formulate the problem as a linear programming model in order to determine the number of units of each product which will maximize the profit.