Until recently, hamburgers at the citys sports arena cost $2.20 each. The food concessionaire sold an average of 9000 hamburgers on game night. When the price was raised to $2.90, the hamburger sales dropped off to an average 5500 sold per night.

a. Assuming a linear demand curve, find the price of a hamburger that will maximize nightly hamburger revenue.

b. If the concessionaire had fixed costs of $1000 per night, and a variable cost of $0.70 per hambuger, find the price of a hamburger that will maximize the nightly profit.