CBSE Class 12 · 2019 · Linear ProgrammingLong Answer

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A company produces two types of goods A and B that require gold and silver. Each unit of type A requires 3 g of silver and 1 g of gold while that of type B requires 1 g of silver and 2 g of gold. The company can use at most 9 g of silver and 8 g of gold. If each unit of type A brings a profit of Rs. 40 and that of type B Rs. 50, find the number of units of each type that the company should produce to maximize the profit. Formulate and solve the LPP graphically and also find the maximum profit.

Answer: Max profit = Rs 230 at (2, 3): 2 units of A and 3 units of B

Solution

Let

x

units of type A and

y

units of type B be produced.
Profit:

P = 40 x + 50 y

.
Silver:

3 x + y \leq 9

Gold:

x + 2 y \leq 8

x \geq 0, y \geq 0

Corner points:

(0, 0)

(3, 0)

(2, 3)

(intersection of

3 x + y = 9

and

x + 2 y = 8

) and

(0, 4)

.
Evaluate

P = 40 x + 50 y

(3, 0)

P = 120

(2, 3)

P = 80 + 150 = 230

← maximum

(0, 4)

P = 200

∴ P_{m a x} = Rs 230 at (2, 3)

2 units of type A and 3 units of type B give the maximum profit of Rs 230.

CBSE Class 12 Board · 2019 · Subjective

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CBSE Class 12 · 2019 · Linear ProgrammingLong Answer

Solution

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