In order to simplify assume that there are only two states o

In order to simplify, assume that there are only two states of nature, Low and High demand, and the owner has decided to either order 2 lots or 3 lots. The payoffs (profits) table is as follows:

                                                Demand

Order Size                   Low (S1)        High(S2)

2 Lots                             9                     35

3 Lots                              6                     60

Under what range of probabilities should a person choose 2 Lots versus 3 Lots?

Now, assume you have found a fairly reliable source to predict the demand for merchandise and you estimate the following conditional probabilities:

                                    Demand

Order Size                   Low (S1)        High(S2)

2 Lots                             9                     35

3 Lots                              6                     60

P(F/High) =.85        P(U/High)=.15

P(F/Low) =.10        P(U/Low)=.90

Note: A favorable response will indicate a high demand.

What is the value of this sample information? Draw your tree? The prior probabilities are P(low) =.6 and p(high)=.4

Solution

Let x = probability of high demand.

Then 1 - x = Probability of Low Demand.

9x + (35)(1 - x) = 6x + 60(1 - x)

9x + 35 - 35x = 6x + 60 - 60x

-24x + 35 = -54x + 60

30x = 25

x = 5/6 = 0.8222

Therfore, when there is 82.222% probability of high demand, the owner should order 3 lots. If the probability of high demand is less, then the owner should order two lots.