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CAT-2007-Previous Years Paper

Question
4 out of 25
 

Mr David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs 30. On the other hand, the cost, in rupees, or producing x units is 240 + bx + cx², where b and c are some constants. Mr David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by . However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr David can sell as such as he can produce. His objective is to maximize the profit.


How many units should Mr David produce daily?



A 70

B 150

C 130

D 100

E Cannot be determined

Ans. D

Quantity produced

CP

SP

Profit

x

240+bx+cx2

30x

30x-240-bx-cx2

20

240+20b+400c

600

600-240-20b-400c

40

240+40b+1600c

1200

1200-240-40b-600c

60

240+60b+3600c

1800

1800-240-b+3600c

(i)

Also

(ii)

From (i)

2800c + 20b – 480 = 0 (iii)

200c + 20b – 720 = 0 (iv)

2400c = 240

Profit on x units

i.e.,

f (x) is maximum at x if

2x = 200, or, x = 100

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