D$10($DECISION TABLE $-$ EMV$)$

The owner of a fruit shop in Leeds sells oranges in crates and he needs to decide how many crates of oranges

to purchase each week to sell in his shop. He buys each crate for $20$ and sells it at $35$ per crate. Any

oranges left unsold are returned to the wholesaler who refunds $40\%$ of the original costs. The owner is

considering a stocking strategy of $4,5,6,$ or $7$ crates per week. Table $1$ is the Conditional Profit $($Payoff$)$

table based on the weekly purchase $($stocking strategy$)$ of the oranges he gets, and the number sold $($demand$).$

Table $2$ is the expected values based on the Conditional Profits and probabilities of selling the oranges.

a$)$ Complete both tables.

b$)$ Calculate the expected monetary value $($EMV$)$ for each stocking strategy.

c$)$ What should be the stocking strategy?

The probability distribution $($Prob$.)$ of customer demands are given in table $1$