A company manufactures two types of screws A and B. All the screws have to pass through a threading machine and a slotting machine. A box of Type A screws requires 2 minutes on the threading machine and 3 minutes on the slotting machine. A box of type B screws requires 8 minutes of threading on the threading machine and 2 minutes on the slotting machine. In a week, each machine is available for 60 hours. On selling these screws, the company gets a profit of Rs 100 per box on type A screws and Rs 170 per box on type B screws. Formulate this problem as a LPP given that the objective is to maximise profit.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Max $Z = 100x + 170y$ subject to $x + 4y \leq 1800, 3x + 2y \leq 3600, x, y \geq 0$
Let the company manufactures $x$ boxes of type A screws and $y$ boxes of type B screws.
From the given information, we can construct the following table.
|
Items |
Type A (x) |
Type B (y) |
Minimum time available on each machine in a week |
|
Time required on threading machine |
2 |
8 |
$60 \times 60 = 3600$ minutes |
|
Time required on slotting machine |
3 |
2 |
$60 \times 60 = 3600$ minutes |
|
Profit |
₹100 |
₹170 |
As per the information in the above table, the objective function for maximum profit $Z = 100x + 170y$
Subject to the constraints
$2x + 8y \leq 3600$
$⇒x + 4y \leq 1800 \quad \dots(i)$
$3x + 2y \leq 3600 \quad \dots(ii)$
$x \geq 0, y \geq 0$ (non-negative constraints)
Hence, the required LPP is Maximise $Z = 100x + 170y$
Subject to the constraints,
$x + 4y \leq 1800, 3x + 2y \leq 3600, x \geq 0, y \geq 0$.