Question

A manufacturing company makes two types of television sets; one is black and white and the other is colour. The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a coloured set. The company can spend not more than Rs 648000 a week to make television sets. If it makes a profit of Rs 510 per black and white set and Rs 675 per coloured set, how many sets of each type should be produced so that the company has maximum profit? Formulate this problem as a LPP given that the objective is to maximise the profit.

Answer 1

Let x and y denote, respectively, the number of black and white sets and coloured sets made each week. Thus

x ≥ 0, y ≥ 0

Since the company can make at most 300 sets a week, therefore,

x + y ≤ 300

Weekly cost (in Rs) of manufacturing the set is

1800x + 2700y

and the company can spend upto Rs. 648000. Therefore,

1800x + 2700y ≤ 648000, i.e., or 2x + 3y ≤ 720

The total profit on x black and white sets and y colour sets is Rs (510x + 675y). Let Z = 510x + 675y . This is the objective function.

Thus, the mathematical formulation of the problem is

Maximise Z = 510x + 675y

subject to the constraints :

x + y ≥ 300

2x + 3y ≥ 720

x, y ≥ 0