Suppose that Coca-Cola uses a new type of vending machine that charges a price according to the outside temperature. On hot days, when the temperature is above 77 Farenheit, demand from the vending machine is Q = 300 2P. On cool days, when demand is below 77 Farenheit, demand is Q = 200 2P. The marginal cost of a soda is $0.20.

(a) What price should the machine charge for a soft drink on hot days? What price should it charge on cool days?

(b) Suppose that half the days are hot days and half the days are cool days. If CocaCola uses a traditional vending machine that is simply programmed to charge the same price no matter the temperature, what price should it set?

(c) Compare Coca-Cola's profits from a temperature-sensitive machine to the traditional, uniform pricing machine.