[12 points, 4 points each small question] David decides to treat his group members to pizza for lunch. He forecasts the consumption pattern of his group members shown in the table below. Total Slices of Pizza Probability of Consumption 80 0.2 100 0.3 120 0.2 (140 0.2 160 10.1 (a) Each slice of pizza costs $2. If he runs out of pizza, he has to deal with tired and hungry group members. The associated penalty cost of under ordering is estimated to be $5 per slice short. Leftover slices of pizza are sold to workers from other groups for 50.2 per slice. How many slices should David order? (b) Given the optimal order quantity computed in (a), what is the probability for David to find himself not ordering enough? (c) If David targets at a service level of 95%, what many slices should he order