Until recently, 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

$4.30,

hamburger sales dropped off to an average of

7,000

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

$1,000

per night and the variable cost is

$0.50

per hamburger, find the price of a hamburger that will maximize the nightly hamburger profit.