MegaSports, Inc

Essay

MegaSports, Inc. produces two high-priced metal baseball bats, the Slugger and the Launcher, that are made from special aluminum and steel alloys. The cost to produce a Slugger bat is $100, and the cost to produce a Launcher bat is $120. We can not assume that MegaSports will sell all the bats it can produce. As the selling price of each bat model -- Slugger and Launcher -- increases, the quantity demanded for each model goes down.
Assume that the demand, S, for Slugger bats is given by S = 640 - 4P_S and the demand, L, for Launcher bats is given by L = 450 - 3P_L where P_S is the price of a Slugger bat and P_L is the price of a Launcher bat. The profit contributions are P_S S - 100S for Slugger bats and P_L L - 120L for Launcher bats. Develop the total profit contribution function for this problem.