A firm produces three products A, Band C. It uses two types of raw materials I and II of which 5,000 and 7,500 units, respectively, are available. The raw material requirements per unit of the products are given below:

The labour time for each unit of product A is twice as that of product Band three times that of product C. The entire labour force of the firm can produce the equivalent of 3,000 units. The minimum demand for the three products is 600, 650 and 500 units respectively. Also, the ratio of the number of units produced must be equal to 2 : 3 : 4. Assuming the profits per unit of A, Band Care 50, 50 and 80, respectively, formulate the problem as a linear programming problem in order to determine the number of units of each product which will maximise the profit.

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Requirement per Unit of Product Raw Material A B 3 4 5 3 5 5 10