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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 maximize his profit.
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 maximize his profit.
CBSE | Class 12 | Linear Programming | Maths | NCERT Exemplar
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 maximize his profit.

Solution:

Suppose $\mathrm{x}$ units of type A and $y$ units of type $\mathrm{B}$ electric circuits be produced by the manufacturer. The table is constructed from the information provided:

$$\begin{tabular}{|l|l|l|l|}
\hline Items & Type A $(\mathrm{x})$ & Type B $(\mathrm{y})$ & Maximum stock \\
\hline Resistors & 20 & 10 & 200 \\
\hline Transistors & 10 & 20 & 120 \\
\hline Capacitors & 10 & 30 & 150 \\
\hline Profit & Rs 50 & Rs 60 & $\mathrm{Z}=50 \mathrm{x}+60 \mathrm{y}$ \\
\hline
\end{tabular}$$

So, the total profit function in rupees $\mathrm{Z}=50 \mathrm{x}+60 \mathrm{y}$ is to be maximized with subject to the constraints $20 \mathrm{x}+10 \mathrm{y} \leq 200 \ldots$ (i);
$\quad 10 \mathrm{x}+20 \mathrm{y} \leq 120 \ldots$ (ii)
$10 x+30 y \leq 150 \ldots$ (iii);
$\quad x \geq 0, y \geq 0 \ldots$ (iv)
So, the required LPP is

Maximize $Z=50 x+60 y$ subject to the constraints $20 x+10 y \leq 2002 x+y \leq 20$

$10 x+20 y \leq 120 x+2 y \leq 12$ and $10 x+30 y \leq 150 x+3 y \leq 15, x \geq 0, y \geq 0$

i

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