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 min on the threading machine and 3 min on the slotting machine. A box of type B screws requires 8 min on the threading machine and 2 min on the slotting machine. In a week, each machine is available for 60 h. 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.

Let the company manufactures $x$ boxes of type A screws and $y$ boxes of type B screws.

From the given information,

We have the following conditions as per the question, following corresponding constraint table

Thus, we see that objective function for maximum profit is $Z = 100x + 170y$.

Subject to constraints
$2x + 8y \le 60 \times 60$ [time constraint for threading machine]

$\Rightarrow$ $x + 4y \le 1800$ ……(i)

and $3x + 2y \le 60 \times 60$ [time constraint for slotting machine]

$\Rightarrow$ $3x + 2y \le 3600$ ……..(ii)

Also, $x \ge 0,y \ge 0$

[non-negative constraints] ….(iii)
$\therefore$ Required LPP is,

Maximise $Z = 100x + 170y$

Subject to constraints $x + 4y \le 1800,$ $3x + 2y \le 3600,$ $x \ge 0,$ $y \ge 0$.