Question

2. David buys fruits and vegetables wholesale and retails them at Davids Produce on La Vista Road. One of the 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 20 cents per pound and retails them at 50 cents per pound during the week. Bananas that are more than a week old are too ripe to sell and David will pay workers to take them away. It costs 1 cent to get rid of each pound of unsold bananas. Suppose that the weekly demand for bananas is uniformly distributed between 1000 and 5000 pounds. (a) How many pound of bananas should David order each week? (b) What is the optimal expected weekly profit? (c) Now assume that the demand for bananas is exponentially distributed with mean 3000. How many pound of bananas should be ordered? What is the optimal expected weekly profit? (d) Now suppose that the demand was normally distributed with mean 3000 pounds and variance 500 pounds2. How many pound of bananas should be ordered?

Answer 1

ANSWER:

Given that

David purchases bananas:

At 20 cents per pound and retails them at 50 cents per pound a week at once

Bananas that are more than a week and he will pay workers to take them away

It costs 1 cent to get rid of each pound of unsold bananas

The weekly demand for bananas is uniformly distributed between 1000 and 5000 pounds