Marty vendor is selling programs in front of the stadium of a pro football team that has not had a playoff win in over 11000 days. You have the chance to buy programs from the printer for $0.50 a copy, that you will in turn resell for $1.35. The demand distribution is expected to be normal with a mean = 350 and standard deviation = 70. After the game, any leftover copies will be worthless (nobody will want to remember the game).

a. How many programs should you buy?

b.Based on the optimal quantity (before rounding), what is the approximate probability that you will run out of stock? Think about the service level that you found for part a to identify the optimal quantity (before rounding), and then think about the relationship between thatservice level and the probability of running out of stock (don't overthink this by adjusting for the fact that you rounded your answer for part a).