Until recently hamburgers at the city sports arena cost $4 each. The food concessionaire sold an average of 10,000 hamburgers on a game night. When the price was raised to $4.40, hamburger sales dropped off to an average of 8000 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 has fixed costs of $1000 per night and the variable cost is $.60 per hamburger, find the price of a hamburger that will maximize the nightly hamburger profit.