Question

A machine shop owner is attempting to decide whether to purchase a new drill press, a lathe, or a grinder. The return from each will be determined by whether the company succeeds in getting a government military contract. The profit or loss from each purchase and probabilities associated with each contract outcome are shown in the following payoff table.

Which are the decisions?

Which are the states of nature?

On a separate sheet of paper, draw the decision tree for this problem, paying attention to the proper nodes. You will be drawing an augmented tree later, so this tree should take up 1/3 the page or less.

Calculate the EV for each decision on the right-hand side of the tree.

What is your best decision?

Calculate the EV OF PI. (this means you have to also calculate EV with PI and EV without PI)

Answer 1

Answer :-

- Expected value is - calculated by multiplying each payoff of a decision by the probability of pay-off and then adding these product.

- The probability for each state of nature is given.

- First create an excel spreadsheet with the necessary headings. Then, enter the payoff for each decision based on the contract outcomes.

The resultant values :-

(1) (A) Tool to purchase

(2) (B) States of nature

(3) (B) Contract , No Contract

(4) (A) Purchase; (B) 0.4, 0.6; (C) Expected value.

- It is clear that the greatest project based on the highest expected value is $11,200.

- And company should purchase the "Drillpress".