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.

Question

Philoid · Accepted Answer

Let the manufacturer produces x units of type A circuits and y units of type B circuits. We make the following table from the given data:

Thus according to the table, the profit becomes, Z=50x+60y

Now, we have to maximize the profit, i.e., maximize Z=50x+60y

The constraints so obtained, i.e., subject to the constraints,

20x+10y≤ 200 [this is resistor constraint]

Now will divide throughout by 10, we get

⇒ 2x+y≤ 20…………..(i)

And 10x+20y≤ 120 [this is transistor constraint]

Now will divide throughout by 10, we get

⇒ x+2y≤ 12…………..(ii)

And 10x+30y≤ 150 [this is capacitor constraint]

Now will divide throughout by 10, we get

⇒ x+3y≤ 15…………..(iii)

And x≥0, y≥0 [non-negative constraint]

So, maximize profit, Z=50x+60y,

subject to 2x+y≤ 20,
x+2y≤ 12

x+3y≤ 15

x≥0, y≥0