Question

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 resitors, 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 1

Let the manufacture produces x units of type A circuits and y units of type B circuits. Form the given information, we have following corresponding constraint table.

$\begin{array}{cccc}& \text{Type A (x)}& \text{Type B (y)}& \text{Maximum stock}\\ Resistors& 20& 10& 200\\ Transistors& 10& 20& 120\\ Capacitors& 10& 30& 150\\ Profit& Rs50& Rs60& \end{array}$
Thus, we see that total profit Z =50x +60y (in Rs).
Now, we have following mathematical model for the given problem.
Maximise Z =50x +60 y....(i)
Subject to the constraints.
$20x+10y\le 200$ [resistors constraint]
$\Rightarrow 2x+y\le 20.........\left(ii\right)$
and $10x+20y\le 120$ [transistor constraint]
$\Rightarrow x+2y\le 12........\left(iii\right)$
and $10x+30y\le 150$ [capacitor constraint]
$\Rightarrow x+3y\le 15.......\left(iv\right)$
and $x\ge 0,y\ge 0$ [non-negative constraint]....(v)
SO, maximum Z =50x +60y, subject to $2x+y\le 20,x+2y\le 12,x+3y\le 15,x\ge 0,y\ge 0$