Untilrecently, hamburgers at the city sports arena cost $3.60 each. The food concessionaire sold an average of 14,000 hamburgers on game night. When the price was raised to $4.10, hamburger sales dropped off to an average of 9,000 per night.

(a) Assuming a linear demandcurve, find the price of a hamburger that will maximize the nightly hamburger revenue.

(b) If the concessionaire had fixed costs of $2,000 per night and the variable cost is $0.50 perhamburger, find the price of a hamburger that will maximize the nightly hamburger profit.