Question

2. Now assume that D is a continuous random variable and uniformly distributed between 5 and 9. Find

a)E[max(D,8)]

b)E[(D−8)+]

3. David buys fruits and vegetables wholesale and retails them at Davids Produce on La Vista Road.

One of the more difficult decisions is the amount of bananas to buy. Let us make some simplifying

assumptions, and assume that David purchases bananas once a week at 10 cents per pound and retails

them at 30 cents per pound during the week. Bananas that are more than a week old are too ripe and

are sold for 5 cents per pound.

a) Suppose the demand for the good bananas follows the same distribution as D

given in the first question. What is the expected profit of David in a week if he buys 6 pounds of banana?

b) Now assume that the demand for the good bananas is uniformly distributed between 5 and 9.

How much bananas should David buy each week to maximize his profit? What is the expected

optimal weekly profit?

c) Now assume that the demand for the good bananas follows an exponential distribution with mean 7. How much bananas should David buy each week to maximize his profit?

Answer 1