SOLUTION: If tickets are sold 75$ each then 1800 tickets will be sold for each 1$ increase in tickets price 20 fewer tickets are sold what should be the price of each ticket to max revenue a

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If tickets are sold 75$ each then 1800 tickets will be sold for each 1$ increase in tickets price 20 fewer tickets are sold what should be the price of each ticket to max revenue a      Log On


   

Question 1008041: If tickets are sold 75$ each then 1800 tickets will be sold for each 1$ increase in tickets price 20 fewer tickets are sold what should be the price of each ticket to max revenue and what will it be
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of $1 increases
in ticket price
Let +R+ = revenue from sales of tickets
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+R+=+%28+75+%2B+1%2An+%29%2A%28+1800+-+20n+%29+
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+R+=+135000+%2B+1800n+-+1500n+-+20n%5E2+
+R+=+-20n%5E2+%2B+300n+%2B+135000+
This is a parabola with a peak ( like an upside-down bowl )
The maximum is at +n+=++-b%2F%282a%29+ where:
+a+=+-20+
+b+=+300+
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+-b%2F%282a%29+=+-300+%2F+%28+2%2A%28-20%29+%29+
+-b%2F%282a%29+=+300%2F40+
+-b%2F%282a%29+=+7.5+
Either $7 or $8 added to ticket price maximizes revenue,so
Ticket price should be $82 or $83
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check the answer:
+R+=+%28+75+%2B+1%2An+%29%2A%28+1800+-+20n+%29%0D%0ALet+%7B%7B%7B+n+=+7+
+R+=+%28+75+%2B+1%2A7+%29%2A%28+1800+-+20%2A7+%29+%0D%0A%7B%7B%7B+R+=+82%2A1660+
+R+=+136120+
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Let +n+=+8+
+R+=+%28+75+%2B+1%2A8+%29%2A%28+1800+-+20%2A8+%29%0D%0A%7B%7B%7B+R+=+83%2A1640+
+R+=+136120+
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I get the same revenue on both sides of
the peak, so +n+=+7.5+ must give me
maximum +R+. You can't have 1/2 of a ticket,
so I have to choose +n+=+7+ or
+n+=+8+
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Hope I got it- you should get a 2nd opinion
on this one