A small theater has a seating capacity of 2000.When the ticket price is $20,attendance is 1500.For each $1 decrease in price,attendance increases by 50.The revenue R of the theater as a function of ticket price x is as follows $R ( x ) = - 50 x ^ { 2 } + 2500 x , 10 \leq x \leq 20$ What ticket price will yield a maximum revenue?
A)$55.00 ?
B)$35.00 ?
C)$25.00 ?
D)$45.00 ?
E)$65.00 ?

Question

Quizplus · Accepted Answer

To find the ticket price that yields maximum revenue, we can use the vertex formula for a parabola, $x = -\frac{b}{2a}$, where $a = -50$ and $b = 2500$. Plugging these values in gives $x = -\frac{2500}{2(-50)} = 25$. Therefore, a ticket price of $25 will yield maximum revenue.

A Small Theater Has a Seating Capacity of 2000 R(x)=−50x2+2500x,10≤x≤20R ( x ) = - 50 x ^ { 2 } + 2500 x , 10 \leq x \leq 20R(x)=−50x2+2500x,10≤x≤20

A Small Theater Has a Seating Capacity of 2000 $R ( x ) = - 50 x ^ { 2 } + 2500 x , 10 \leq x \leq 20$