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.

Let the manufacturer produces X units of type A circuits and Y units of type B circuits.

Form the given information, We have the following conditions as per the question, following corresponding constraint table.

Thus, we see that total profit $Z = 50x + 60y$( in Rs.).

Now, We have the following conditions as per the question, the following mathematical model for the given problem.

Maximise $Z = 50x + 60y$ …….(i)

Subject to the constraints. $20x + 10y \le 200\quad$ [resistors constraint]

$\Rightarrow$ $2x + y \le 20$ …….(ii)

and $10x + 20y \le 120$

[transistor constraint]

$\Rightarrow$ $x + 2y \le 12$ ……(iii)

and $10x + 30y \le 150$ [capacitor constraint]

$\Rightarrow$ $x + 3y \le 15$ ……(iv)

and $x \ge 0,y \ge 0$ [non-negative constraint] …(v)

So, maximise $Z = 50x + 60y$, subject to $2x + y \le 20,$ $x + 2y \le 12,$ $x + 3y \le 15,$ $x \ge 0,$ $y \ge 0$.