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 & explanation
Correct answer: option 1
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:
|
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 $10x + 30y ≤ 150$
$⇒x+3y≤15, x ≤0, y ≤0$