CBSE Class 12 · 2011 · Linear ProgrammingLong Answer

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A merchant plans to sell two types of personal computers — a desktop model and a portable model — that will cost Rs. 25,000 and Rs. 40,000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs. 70 lakhs and his profit on the desktop model is Rs. 4,500 and on the portable model is Rs. 5,000. Make an L.P.P. and solve it graphically.

Answer: Max profit = Rs 11,50,000 at (200, 50): 200 desktop and 50 portable models

Solution

Let the merchant stock

x

desktop and

y

portable models.
Profit:

Z = 4500 x + 5000 y

.
Demand:

x + y \leq 250

Investment:

25000 x + 40000 y \leq 7000000 ⟹ 5 x + 8 y \leq 1400

x \geq 0, y \geq 0

Corner points:

(0, 0)

(250, 0)

(200, 50)

(intersection of

x + y = 250

and

5 x + 8 y = 1400

) and

(0, 175)

.
Evaluate

Z = 4500 x + 5000 y

(250, 0)

Z = 1125000

(200, 50)

Z = 900000 + 250000 = 1150000

← maximum

(0, 175)

Z = 875000

∴ Z_{m a x} = Rs 11, 50, 000 at (200, 50)

The merchant should stock 200 desktop and 50 portable models.

CBSE Class 12 Board · 2011 · Subjective

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CBSE Class 12 · 2011 · Linear ProgrammingLong Answer

Solution

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