Question

A manufacturer of electronic circuits has a stock of 200 resistors, 120 transistors and 150 capacitors and is required to produce two types of circuits A and B. Type A requires 20 resistors, 10 transistors and 10 capacitors. Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type A circuit is Rs 50 and that on type B circuit is Rs 60, formulate this problem as a LPP so that the manufacturer can maximize his profit.

Answer 1

Let x units of type A and y units of type B electric circuits be produced by the manufacturer.

From the given information the below table is constructed:

Now, the total profit function in rupees Z = 50x + 60y is to be maximized with subject to the constraints

20x + 10y ≤ 200 … (i); 10x + 20y ≤ 120 … (ii)

10x + 30y ≤ 150 … (iii); x ≥ 0, y ≥ 0 … (iv)

Therefore, the required LPP is

Maximize Z = 50x + 60y subject to the constraints

20x + 10y ≤ 200 2x + y ≤ 20;

10x + 20y ≤ 120 x + 2y ≤ 12 and

10x + 30y ≤ 150 x + 3y ≤ 15, x ≥ 0, y ≥ 0.