Question

Management at Washington Hospital Center is thinking about two investments. One is an MRI machine, which can make $100,000 in good economic conditions or $60,000 in bad economic conditions. Another is a CT scanner, which can make $150,000 in good economic conditions of $10,000 in bad economic conditions. Thus the decision depends on the economic conditions. What is the probability of good economic conditions that equates the two investments?

1. Develop a payoff table for this situation:
2. Find the following:

1. Maximax

2. Maximin

3. Equal likihood

3. 4. Minimum regret

Create a sensitivity graph comparing the different alternatives as the probability of economic conditions changes.

I need a sensitivity graph to compare the different alternatives as the probability of economic conditions changes.

Answer 1

a.

The payoff table is shown below

b.

1.

The max of each decision is 100000 and 150000. Among them the maximum value is with 150000. This means the best decision is CT scanner using maximax criteria.

2.

The min of each decision is 60000 and 10000. Among them the maximum value is 60000. This means the best decision is MRI machines.

3.

The average value of each decision is (100000+60000)/2 =80000 and (150000+10000)/2 = 80000. The equal likelihood decision provides the same value. So either of the decision can be chosen.

4.

The regret table is shown below

The maximum regret of each decision is 50000. This means using minimum regret approach can choose either of the decisions.

The probability of good economy where the both = X then we can solve for X by

100000*X + 60000*(1-X) = 150000*X + 10000*(1-X)

60000 – 40000X = 10000 + 140000X

50000 = 100000X

X = 0.5

At 50% probability, the two investments are equal.

The senstivity graph is shown below

Chart 1 x for e nim moliens B C D E F G H I J K L M N O P R S Sensitivity - MRI machine CT scanner 160000 140000 10 120000 12 100000 14 15 16 80000 60000 40000 20000 Good economy Poor economy