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.

Max $Z = 50x + 60y$
subject to $2x + y \leq 20, x + 2y \leq 12, x + 3y \leq 15, x, y \leq 0$

The correct answer is Option (1) → Max $Z = 50x + 60y$ subject to $2x + y \leq 20, x + 2y \leq 12, x + 3y \leq 15, x, y \leq 0$

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:

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 $10x + 30y ≤ 150$

$⇒x+3y≤15, x ≤0, y ≤0$