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A person sells clothes. At the price of $20, he can sell 100

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Senior Manager
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A person sells clothes. At the price of $20, he can sell 100 [#permalink] New post 04 Aug 2006, 22:55
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A
B
C
D
E

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A person sells clothes. At the price of $20, he can sell 100 clothes. For each dollar the price decreases, 10 more clothes will be sold. What can be his maximun revenue to obtain?
A. 2000
B. 2240
C. 2250
D. 2270
E. 2300
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Last edited by freetheking on 05 Aug 2006, 00:20, edited 2 times in total.
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 [#permalink] New post 04 Aug 2006, 23:52
20*100=2000
19*110=2090
18*120=2160
17*130=2210
16*140=2240
15*150=2250
14*160=2240
so at price of 15 the revenue would be max 2250
Senior Manager
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Re: PS:Maximun revenue [#permalink] New post 05 Aug 2006, 00:13
How about following approach??

F(n) = (20-n)(100+10n)

F(n) = 2000+100n-10n^2
= -10(n^2-10n-200)
= -10[(n-5)^2-225] (concave down.. when n=5 maximun value)

F(5) = -10*-225 = 2250
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Last edited by freetheking on 05 Aug 2006, 00:21, edited 1 time in total.
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 [#permalink] New post 05 Aug 2006, 00:16
Not bad, but the Q asks about the PRICE not the revenue
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Re: PS:Maximun revenue [#permalink] New post 05 Aug 2006, 13:25
freetheking wrote:
A person sells clothes. At the price of $20, he can sell 100 clothes. For each dollar the price decreases, 10 more clothes will be sold. What can be his maximun revenue to obtain?
A. 2000
B. 2240
C. 2250
D. 2270
E. 2300


@ $20 Revenue =2000
@ $19 Revenue =2090 (19*110)
@ $18 Revenue =2160 (18*120)
@ $17 Revenue =2210 (17*130)
@ $16 Revenue =2240 (16*140)
@ $15 Revenue =2250 (15*150)

Hence C

Heman
Re: PS:Maximun revenue   [#permalink] 05 Aug 2006, 13:25
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A person sells clothes. At the price of $20, he can sell 100

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