In: Math
1. Until recently hamburgers at the Erwin Center cost $2 each. The food concessionaire sold an average of 10,000 hamburgers on a game night. When the price was raised to $2.40, hamburgers sales dropped off to an average of 8,000 per night. (a) Find the price of a hamburger that will maximize the nightly hamburger revenue. (b) Suppose that the concessionaire has fixed costs of $1,000 per night and the variable cost is $0.60 per hamburger. Find the price of a hamburger that will maximize the nightly hamburger profit.
2. A manufacturer needs to make a cylindrical can that will hold 1.5 liters of liquid. Determine the dimensions of the can that will minimize the amount of material (top, bottom, and sides) used in its construction.