R(x) =

(b) What ticket price will yield a maximum revenue?

$

What is the maximum revenue?

(a) Write the revenue R of the theater as a function of ticket price x.

R(x) =

(b) What ticket price will yield a maximum revenue?

$

What is the maximum revenue?

R(x) =

(b) What ticket price will yield a maximum revenue?

$

What is the maximum revenue?

Tutors, sign in to answer this question.

Letting x represent the change in ticket price in dollars:

R(x) = (20-x)(1500 + 100x);** 0≤ x ≤ 5 x cannot go higher than 5**

R(x) = 30000 + 2000x - 1500x - 100x^{2}

Find the vertex of the parabolic function:

Vertex: (-b/2a, r(-b/2a)); a = -100, b=500

-b/2a = -500/-200 = 2.5

r(2.5) = -100(2.5)^{2} + 500(2.5) + 30000

= -625 + 1250 + 30000

= $30,625

The maximum revenue is at the point where ticket prices are

reduced by $2.5 to $17.50. The revenue at that point is $30,625

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## Comments

r(x) = xa

Price Attendance Revenue

_______________________________

20 1500 $30,000

19 1600 $30,400

18 1700 $30,60017 1800 $30,60016 1900 $30,400

15 2000 $30,000

17.5(1750) = $30,625 revenue.