Question

S1.16. (LO S1.1) The Midtown Market purchases apples from a local grower. The apples are purchased on Monday at $1.00 per kg, and the market sells them for $1.50 per kg. Any apples left over at the end of the week are sold to a local zoo for $0.25 per kg. The possible demands for apples and the probability for each are as follows.

Demand (kg)	Probability
10	0.10
10.5	0.20
11	0.30
11.5	0.30
22	0.10

1. a. The market must decide how many apples to order in a week. Construct a payoff table for this decision situation and determine the amount of apples that should be ordered using expected value.
2. b. Assuming that probabilities cannot be assigned to the demand values, what would the best decision be using the maximax and maximin criteria?

Answer 1

a) Expected order value =

= 10*0.1 + 10.5*0.2 + 11*0.3 + 11.5 *0.3 + 22*0.1

= 1 + 2.1 + 3.3 + 3.45 + 2.2

= 12.05

= 12 apples

Payoff = 12 * $0.5

= $6 Answer

b) Maximax means maximise the maximum profit:

So according to it to maximize it, we should buy 22 apples, as that's the largest demand that's possible, which will give a maximum of profit of $11.i.e. (22*$0.5)

The maximin decision rule suggests that a decision maker should select the alternative that offers the least unattractive worst outcome.

So here payoff = Minimum demand * profit per apple

= 10 * 0.5

= $5