Question

A company manufactures two types of screws A and B. All the screws have to pass thorugh 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.

Answer 1

Let the company manufactures x boxes of type A screws and y boxes of tyep B screws. Form the given information, we have following corresponding constraint table

$\begin{array}{cccc}& \text{Type A(x)}& \text{Type B(y)}& \text{Maximum time available}\\ & & & \text{on each machine in a}\\ & & & \text{week}\\ \text{Time required for scres}& 2& 8& 60\times 60\left(min\right)\\ \text{on threading machine}& & & \\ \text{Time required for screws}& 3& 2& 60\times 60\left(min\right)\\ \text{on slotting machine}& & & \\ \text{Profity}& \text{Rs 100}& \text{Rs 170}& \end{array}$Thus, we see that objective function for maximum profit is Z =100x+170y.
Subject to constraints
$2x+8y\ge 60\times 60$ [time constraint for threading machine]
$\Rightarrow x+4y\le \mathrm{1800.....}\left(i\right)$
and $3x+2y\le 60\times 60$ [time constraint for slotting machine]
$\Rightarrow 3x+2y\le 3600.....\left(ii\right)$
Also, $x\ge 0,y\ge 0$ [non-negative constraints]....(iii)
$\therefore$ Required LPP is
maximum Z =100x+170y
Subject to constraints $x+4y\le 1800,3x+2y\le 3600,x\ge 0,y\ge 0.$