How do I answer these?

Question

At a price of $7.75 per ticket, a musical theater group can fill every seat in their 1700 seat performance hall. For every additional dollar charged for admission, the number of tickets sold drops by 95. a) What ticket price maximizes revenue? Round your answer to the nearest cent. price = $

b) How many seats are sold at that price? Round your answer to the nearest whole number. number of seats sold =

Answer 1

(1700, 7.75) and (1605, 8.75) are two points on the demand curve

the curve has a slope = - 1/95 = (P-7.75)/(x - 1700)

x -1700 = - 95P + 736.25

x = 2436.25 - 95P

Revenue = R = xP = 2436.25P - 95P^2

R' = 2436.25 - 190P = 0

P = 2436.25/190 = $12.82 ticket price to maximize revenue

the intercepts are x=2436.25 and $25.64

graphically the revenue maximizing price is the midpoint on the demand curve or half of $25.64 = $12.82

Answer 2

d represents each $1 increase

R(d) = (1700 - 95d)(7.75 + d)

Expnad and either put into vertex form or take first derivative.