Downtown Health Clinic needs to order influenza vaccines for the next flu season. The Clinic charges its patients $15.00 per vaccination and each dose of vaccine costs the clinic $4.00 to purchase. The Center for Disease Control has a long standing policy of buying back unused vaccines for $1.00 per dose. The Clinic estimates the following probability distribution for the season’s demand:

Demand Probability

2,000 .......0.05

3,000 .......0.20

4,000 .......0.25

5,000 .......0.40

6,000 .......0.10

a. How many vaccines should the Clinic order to maximize its expected profit?

b. The Clinic is trying to determine if they should participate in a new Federal program in which the cost of each dose is reduced to $2.00. However, to participate in the program, they can charge no more than $10.00 per vaccine. On strictly a profit maximizing basis, should the Clinic agree to participate?