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Two hundred people will attend a university fund-raiser if tickets cos
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02 Sep 2021, 03:41
02 Sep 2021, 03:41
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Question Stats:
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Two hundred people will attend a university fund-raiser if tickets cost $30 per person. For each $15 increase in ticket price, 25 fewer people will attend. What ticket price will yield the maximum amount of money for the university?
(A) $30
(B) $45
(C) $60
(D) $75
(E) $90
(A) $30
(B) $45
(C) $60
(D) $75
(E) $90
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Joined: 19 Nov 2020
Posts: 326
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GRE 1: Q160 V152
Two hundred people will attend a university fund-raiser if tickets cos
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03 Sep 2021, 16:43
03 Sep 2021, 16:43
1
This is inverse linear relationship between price and demand (P, D) defined with slope for values (30,200) and (45,175)
(200-175)/(30-45)=-25/15=-5/3
D=-5P/3 + C, where C is constant aka demand intercept
200=-5*30/3 + C, C=250
We should maximize revenue, D*P ---> P*(-5P/3+250).
Derivative of \(-5P^2/3+250P\) equated to 0 will maximize the revenue.
\(-10P/3+250=0\), \(10P=750\), \(P=75\) and answer is D
(200-175)/(30-45)=-25/15=-5/3
D=-5P/3 + C, where C is constant aka demand intercept
200=-5*30/3 + C, C=250
We should maximize revenue, D*P ---> P*(-5P/3+250).
Derivative of \(-5P^2/3+250P\) equated to 0 will maximize the revenue.
\(-10P/3+250=0\), \(10P=750\), \(P=75\) and answer is D
Carcass wrote:
Two hundred people will attend a university fund-raiser if tickets cost $30 per person. For each $15 increase in ticket price, 25 fewer people will attend. What ticket price will yield the maximum amount of money for the university?
(A) $30
(B) $45
(C) $60
(D) $75
(E) $90
(A) $30
(B) $45
(C) $60
(D) $75
(E) $90
Re: Two hundred people will attend a university fund-raiser if tickets cos
[#permalink]
03 Sep 2021, 21:23
03 Sep 2021, 21:23
1
Simply check each option
A. 30x200=6000
B. 45x175= 7875
C. 60x150= 9000
D. 75x125= 9375
E. 90x100= 9000
Answer: D
A. 30x200=6000
B. 45x175= 7875
C. 60x150= 9000
D. 75x125= 9375
E. 90x100= 9000
Answer: D
