Question

[PLEASE NO UNRELATED COPY/PASTE SOLUTION ABOUT ELASTICITY]

Suppose a vending machine has only one type of drink. The machine can hold 600 cans. Mean demand is ? = 20 cans per day and demand during a period of m days is well-approximated as a U[0.75m? ,1.25m? ] distribution. The machine does not sell fractions of cans. It costs Coca-Cola 40 cents to manufacture each can of soda. The vending machine price is $1.50 per can. The estimated cost of a restock trip is $30.00, not including the cost of the cans placed in the machine. Assume that the vending machine will be filled to capacity each time it is restocked. Coca-Cola sets a proxy penalty cost of 70 cents for each can of unmet demand. This artificial cost is independent of the failure to earn profit from the sale of a can. It represents the long-term cost of customer dissatisfaction from an empty vending machine, and pretend that there are 360 days in a year.

Without a sensor, Coca-Cola only has the distributional information given above. Find the expected annual profit if Coca-Cola’s policy is to restock the machine every m = 30 days (the penalty for unmet demand is part of the cost).

Answer 1