How did you find the slope

Question

The Wave Hotel offers luxury suites on Cocoa Beach. It has 200 beachfront suites. At the current price of $300 per night for each suite, it is fully occupied. A recent marketing study indicates that for every $10 increase in price, 5 fewer suites will be booked. (For example, if the price is $310, then 195 suites are booked. If the price is $320, then 190 suites are booked.)

The marketing group recommends that the Wave Hotel charge $300 per night for each suite to maximize the revenue.

Did the marketing group make a correct recommendation? Hint: Revenue is the total amount of money brought in.

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Raymond B. answered • 06/16/21

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(200, 300), (195, 310) are two points on the demand curve

it has slope = -10/5 = -2

Answer 1

(200,300),(195,310) are two points on the demand curve

it has slope = -10/5 =-2 = (y-300)/(x-200)

y=-2x +700

P =-2x +700

R =Px = -2x^2 +700x

R' = -4x +700 = 0

x = 700/4 = 175 =Revenue maximizing output level with Price = 700-350= $350

which is the point (175,350)

the marketing division was a little off on their recommendation of P=$300, x=200

with P=300, R= 700(200)-2(200^2) = 140,000-80,000 = $60,000 in Revenue

while with P=350, R = 700(175)-2(175)^2 = 122,500- 61250 = $61,250 in Revenue

which is $250 greater when Price = $350 than with Price = $300 per night