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Until​ recently, hamburgers at the city sports arena cost ​$3.20 each. The food concessionaire sold an...

Until​ recently, hamburgers at the city sports arena cost ​$3.20 each. The food concessionaire sold an average of 18,000 hamburgers on game night. When the price was raised to $3.80, hamburger sales dropped off to an average of 12,000 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 2,000 per night and the variable cost is ​$0.40 per​ hamburger, find the price of a hamburger that will maximize the nightly hamburger profit.

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

The hamburger price that will maximize the nightly hamburger revenue is ​$__.

​(Round to the nearest cent as​ needed.)

Math   Calculus   
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