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When a swimming park owner charges $4.00 for admission, there is an average attendance of 100 people. For every $0.20 increase in the admission price, there is a loss of 2 customers from the average number. What admission price should be charged in order to maximize revenue $?

Respuesta :

osaruevbuomwan

Answer:

$490

Explanation:

Let xR be the revenue function

xR = (4 + 0.2(x))(100 - 2x) = 400 + 12x - 2x²/5

Maximum revenue occurs when xR = 0:

xR = 12 - 4x/5 = 0

x = 15

Admission price = 4 + (0.2*15) = 4 + 3 = $7

Max revenue = $7 * (100 - (15*2) = 7 *70  = $490

Tundexi

An amount of $490 is the admission price that should be charged in order to maximize revenue.

Let xR represent the revenue function

xR = (4 + 0.2(x))(100 - 2x)

XR= 400 + 12x - 2x²/5

Generally, a maximum revenue occurs when xR = 0:

xR = 12 - 4x/5 = 0

x = 15

What is the admission price?

= 4 + (0.2*15)

= 4 + 3

= $7

What is Maximum revenue?

= $7 * (100 - (15*2)

= 7 *70

= $490

In conclusion, the amount of $490 is the admission price that should be charged in order to maximize revenue.

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