The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by q = (101 − 2p)2

Question

The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by q = (101 − 2p)²,

 where p is the price per dumbbell, and q is the demand in weekly sales. Find the price Professor Schwarzenegger should charge for his dumbbells to maximize revenue. (Round your answer to the nearest cent.)

$___

Answer 1

q = (101 - 2p)^2 = 101^2 - 404p + 4p^2

R = pq = revenue

max revenue = $76,318.59

selling 4,535 dumb bells per week

at price = $16.83 per dumb bell

q = (101 - 2(16.83)^2 = (101 - 33.66)^2 = 67.34^2 = 4534.68

maximum revenue = 4535 x 16.83 = $76,318.59