EcoTable is a retailer of specialty organic and ecologically friendly foods. In one of their Cambridge, Massachusetts, stores, they plan to offer a gift basket of Tanzanian teas for the holiday season. They plan on placing one order and any leftover inventory will be discounted at the end of the season. Expected demand for this store is 4.5 units and demand should be Poisson distributed. The gift basket sells for $55, the purchase cost to EcoTable is $32, and leftover baskets will be sold for $20.
a. If they purchase only 3 baskets, what is the probability that some demand will not be satisfied?
b. If they purchase 10 baskets, what is the probability that they will have to mark down at least 3 baskets?
c. How many baskets should EcoTable purchase to maximize its expected profit?
d. Suppose they purchase 4 baskets. How many baskets can they expect to sell?
e. Suppose they purchase 6 baskets. How many baskets should they expect to have to mark down at the end of the season?
f. Suppose EcoTable wants to minimize its inventory while satisfying all demand with at least a 90 percent probability. How many baskets should they order?
g. Suppose EcoTable orders 8 baskets. What is its expected profit?