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A salesperson sells shoes. At a price of $32, he can sell 80 [#permalink] ### Show Tags 12 Sep 2008, 05:43 00:00 Difficulty: (N/A) Question Stats: 0% (00:00) correct 100% (03:01) wrong based on 1 sessions ### HideShow timer Statistics This topic is locked. If you want to discuss this question please re-post it in the respective forum. A salesperson sells shoes. At a price of$32, he can sell 80 pairs of shoes. For every 2 dollars discount on the price of the shoes, 20 more pairs of shoes are sold. At what price will the salesperson have the highest revenue from shoe sales.

$32$27
$24$21
$20 SVP Joined: 07 Nov 2007 Posts: 1820 Location: New York Followers: 34 Kudos [?]: 867 [0], given: 5 Re: Zumit PS 014 [#permalink] ### Show Tags 12 Sep 2008, 20:40 dancinggeometry wrote: A salesperson sells shoes. At a price of$32, he can sell 80 pairs of shoes. For every 2 dollars discount on the price of the shoes, 20 more pairs of shoes are sold. At what price will the salesperson have the highest revenue from shoe sales.

$32$27
$24$21
$20 What is "ZUMIT?" Is it zoom it? _________________ Your attitude determines your altitude Smiling wins more friends than frowning VP Joined: 17 Jun 2008 Posts: 1397 Followers: 8 Kudos [?]: 290 [0], given: 0 Re: Zumit PS 014 [#permalink] ### Show Tags 14 Sep 2008, 02:28 dancinggeometry wrote: A salesperson sells shoes. At a price of$32, he can sell 80 pairs of shoes. For every 2 dollars discount on the price of the shoes, 20 more pairs of shoes are sold. At what price will the salesperson have the highest revenue from shoe sales.

$32$27
$24$21
$20 IMO E 32*80 = revenue in norml scenario acc to this ques ,say we decrease the shoe sales n times by 2 dollars,20n additional pair of shoes sold ,hence new revenue is (32-2n)(80+20n)=R R is max when n=6 hence 32-2*6=20$ is the answer
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14 Sep 2008, 23:03
spriya wrote:
IMO E
32*80 = revenue in norml scenario
acc to this ques ,say we decrease the shoe sales n times by 2 dollars,20n additional pair of shoes sold ,hence new revenue is
(32-2n)(80+20n)=R
R is max when n=6 hence 32-2*6=20 $is the answer Good explanation. But, how did you arrive at n = 6 for R to be the max? SVP Joined: 07 Nov 2007 Posts: 1820 Location: New York Followers: 34 Kudos [?]: 867 [0], given: 5 Re: Zumit PS 014 [#permalink] ### Show Tags 15 Sep 2008, 00:02 scthakur wrote: spriya wrote: IMO E 32*80 = revenue in norml scenario acc to this ques ,say we decrease the shoe sales n times by 2 dollars,20n additional pair of shoes sold ,hence new revenue is (32-2n)(80+20n)=R R is max when n=6 hence 32-2*6=20$ is the answer

Good explanation. But, how did you arrive at n = 6 for R to be the max?

(32-2n)(80+20n)=R = 2(16-n)*20*(4+n)
= 80(-n^2+12n+20)

f(n)=(-n^2+12n+20)
derivative of f(n)=f'(n)=-2n+12=0 ( n is max or min)
n=6
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16 Sep 2008, 12:43
dancinggeometry wrote:
A salesperson sells shoes. At a price of $32, he can sell 80 pairs of shoes. For every 2 dollars discount on the price of the shoes, 20 more pairs of shoes are sold. At what price will the salesperson have the highest revenue from shoe sales.$32
$27$24
$21$20

the premisis of the question is specefying ( for every 2 dollars discount ) thus the answer has to be even.( 32 - 24 - 20)

however 32 is obviously ruled out

then it is either ( 24 - 20) just substitute and compare

the first 80 shoes are not relevent thus we need to calculate the excess in rev from additional sales due to discount. ie:

- 24*(20*4) = 1920

- 20 *(20*5) = 2000
Re: Zumit PS 014   [#permalink] 16 Sep 2008, 12:43
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