1. SOCIAL ENTREPRENEURSHIP: Your student organization wants to raise some money to donate to a favorite charity, so you decide to put on a spring benefit show. Even though you are technically \"not for profit\" for tax purposes, you still want to raise as much money as you can for the cause, so you act like a profit-maximizing firm. Consider how you should act under various scenarios. a. Assume that the demand for tickets to your show is given by P[Q] = 40 l Q and that your only costs are the 300 you must pay to rent the theatre. Compute your profit-maximizing price (P*), quantity (Q*) and Profit (3*). b. Suppose instead that the demand curve is actually nonlinear and all costs disappear (covered by a mysterious and generous benefactor). Specifically, P[Q] = 75 Q2, which implies that total revenue is TR[Q] = Q*P[Q] = Q(75 Q2) = 75Q Q3, and then marginal revenue is MR[Q] = dTR/dQ = 75 3Q2. Compute your prot-maximizing price (P*), quantity (Q*) and Profit (*). TIPS: If all costs are zero, then how is profit related to revenue? How could you nd the highest point of a hill- shaped curve? For a picture of TR, try Googling graph 75xxA3