Until recently, hamburgers at the city sports arena cost $5.50 each. The food concessionaries sold an average of 6,250 hamburgers on game night. When the price was raised to $6.50, hamburger sales dropped off to an average of 4,500 per night.
(a) Assuming a linear demand curve, find the price of a hamburger that will maximize the nightly hamburger revenue.
(b) If the concessionaire had fixed costs of $2,500 per night and the variable cost is $0.70 per hamburger, find the price of a hamburger that will maximize the nightly hamburger profit.