5. [10 points] Javier plans to make and sell his own all-natural shampoo. The graph below shows the marginal cost M C' (q), in dollars per liter, of (1 liters of shampoo. In order to start making shampoo, Javier must rst spend $25 on supplies, but he has no other xed costs. 3; 12 10 2' y=MC(Q) g 10 20 30 40 50 60 70 80 Javier can sell up to 50 liters of shampoo for $10 per liter. Any additional shampoo can be sold to a local salon for $4 per liter. Throughout this problem, you do not need to show work. a. [2 points] On the axes above, carefully sketch the graph of the marginal revenue M R(q), in dollars per liter, of 1:; liters of shampoo. Solution: See above. b. [1 point] At what value(s) of q in the interval [0,80] is marginal cost maximized? Answer: 10 c. [1 point] At what value(s) of q in the interval [0,80] is cost maximized? Answer: 80' d. [2 points] At which values of g in the interval [0, 80] is prot increasing? Give your answer as one or more intervals. Answer: (20, 70) e. [1 point] How many liters of shampoo should Javier make in order to maximize his prot? Answer: 70