1. (Revenue management with marginal costs) You have designed and produced a new widget and the demand is equal to D(p)=3/5(300-p). The cost of producing one item is equal to $100. • If given cost, optimize Profit (not Revenue)
• There are two equations for Profit, given marginal cost (you can use either):
o Profit = Demand X (Profit Margin), where Profit Margin = (p – c), OR
o Profit = Revenue – (Total Cost), where Total Cost = Demand x (Marginal Cost)

a) What is the optimal price that maximizes profits? In class we used the same equation for D(p) and found the optimal price to maximize revenue was $150. Is the price to maximize profit the same as the price to maximize revenue?
b) How much is the optimal revenue?
c) If capacity is 100, should I change the price? If so, what is the new price?
d) If capacity is 30, should I change the price? If so, what is the new price?