I have listed a homework problem below that I have been working on. How do I get the expected number sold/expected number unsold/expected number lost if I do not have the pdf for the demand? Am I supposed to derive a pdf from the information given in the problem? In the example problems in my textbook, It usually says that the demand is 18, so it is easy to work the problem out. This is supposed to be a profit maximization problem.
David buys fruits and vegetables wholesale and retails them at David’s 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 25 cents per pound and retails them at 60 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 4 cent to get rid of each pound of unsold bananas. Suppose that the weekly demand for bananas is uniformly distributed between 1000 and 2000 pounds.
a) Assume David orders 1500 pound of bananas each week, calculate the expected number of sold bananas, expected number of unsold bananas, expected number of lost sale, and the expected weekly profit.
(f) (R Simulation) Again, let n be the number of random demands you will generate. Test the policy you obtained in (e) for n = 10, 100, 1000, 100000, where the demand for bananas is exponentially distributed with mean 1500. Write down your code, compare your result with question (e) and explain your findings. you may use “rexp(n, rate = 1/1500)” to generate exponential random variable