ACCA PM · Guided practice (Show me how)
Chapter 10: Risk and Uncertainty
Payoff tables: expected value, maximin, maximax, minimax regret and perfect information
John has a factory capacity of 1,200 units per month. Units cost him $6 each to make and his normal selling price is $11 each. However, the demand per month is uncertain and is as follows:
| Demand | Probability |
|---|---|
| 400 | 0.2 |
| 500 | 0.3 |
| 700 | 0.4 |
| 900 | 0.1 |
He has been approached by a customer who is prepared to contract to a fixed quantity per month at a price of $9 per unit. The customer is prepared to sign a contract to purchase 300, 500, 700 or 800 units per month.
The company can vary production levels during the month up to the maximum capacity, but cannot carry forward any unsold units in inventory.
(a) Calculate all possible profits that could result. (b) Determine for what quantity John should sign the contract under each of: (i) expected value, (ii) maximin, (iii) maximax, (iv) minimax regret. (c) What is the most that John would be prepared to pay in order to obtain perfect knowledge as to the level of demand?
(a) The profit table
Prepare the missing entries in John's monthly profit table.
(b)(i) Expected value
Calculate John's expected monthly profits for the specified contracts and state the contract size selected by expected value.
(b)(ii)-(iii) Maximin and maximax
State John's monthly contract sizes selected by maximin and maximax.
(b)(iv) Minimax regret
Calculate John's worst monthly regret for the specified contract and state the contract size selected by minimax regret.
(c) The value of perfect information
Calculate John's expected monthly profit with perfect information and the value of that information.
Opening this exercise…