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Home » A manufacturer of electronic circuits has a stock of     resistors,     transistors and     capacitors and is required to produce two types of circuits A and B. Type A requires     resistors,     transistors and     capacitors. Type B requires     resistors,     transistors and     capacitors. If the profit on type A circuit is Rs     and that on type B circuit is Rs     , 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 | Exercise 1 | 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.

Let x units of type A and y units of type B electric circuits be produced by the manufacturer.

From the given information the below table is constructed:

Now, the total profit function in rupees

    \[Z\text{ }=\text{ }50x\text{ }+\text{ }60y\]

is to be maximized with subject to the constraints

    \[20x\text{ }+\text{ }10y\le 200\]

… (i);

    \[10x\text{ }+\text{ }20y\le 120\]

… (ii)

    \[10x\text{ }+\text{ }30y\le 150\]

… (iii);

    \[x\ge 0,\text{ }y\ge 0\]

… (iv)

Therefore, the required LPP is

Maximize

    \[Z\text{ }=\text{ }50x\text{ }+\text{ }60y\]

subject to the constraints

    \[20x\text{ }+\text{ }10y\le 200\text{ }2x\text{ }+\text{ }y\le 20\]

;

    \[10x\text{ }+\text{ }20y\le 120\text{ }x\text{ }+\text{ }2y\le 12\]

and

    \[10x\text{ }+\text{ }30y\le 150\text{ }x\text{ }+\text{ }3y\le 15,\text{ }x\ge 0,\text{ }y\ge 0\]

.

i

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