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 maximise his profit.

Answer 1

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

As per the given information, we construct the following table:

Items	Type A (x)	Type B (y)	Maximum stock
Resistors	20	10	200
Transistors	10	20	120
Capacitors	10	30	150
Profit	₹ 50	₹ 60	Z = 50x + 60y

Now, we have the total profit in rupees Z = 50x + 60y to maximise subject to the constraints

20x + 10y ≤ 200  .....(i)

10x + 20y ≤ 120  ......(ii)

10x + 30y ≤ 150  ......(iii)

x ≥ 0, y ≥ 0   ......(iv)

Hence, the required LPP is

Maximise 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