Question

11) The Gorman Manufacturing Company must decide whether to purchase a component from a supplier or manufacture the component at its Milan, Michigan plant. If demand is high, Gorman could profitably purchase the component. However, if demand is low, Gorman’s unit manufacturing cost would be high due to underutilization of equipment. The following table shows the projected profit (in thousands of dollars) for Gorman’s decision.

                                                                                    DEMAND

                                                           

                                                                        Low                  Medium             High                

                                                           

            Manufacture the Component                      -20                    40                     100

            Purchase the component                            10                    45                     70

Suppose that it is estimated that the probabilities of the three demand possibilities are P(low)=.40, P(medium)=.35, and P(high)=.25.

A test market study of the potential demand for the product is expected to report either a favorable or unfavorable market condition. The following conditional probabilities have been estimated by Gorman.

            P (favorable|low)=.10         P(unfavorable|low)=.90

            P(favorable|medium)=.40 P(unfavorable|medium)=.60

            P(favorable|high)=.60       P(unfavorable|high)=.40

a) What is the conditional probability of low demand given a favorable condition is reported?

b) What is the conditional probability of medium demand given a favorable condition is reported?

c) What is the conditional probability of high demand given a favorable condition is reported?

d) If Gorman receives a report suggesting a favorable condition, should they purchase or manufacture the component?

e) If Gorman receives a report suggesting an unfavorable condition, should they purchase or manufacture the component?

f) What is Gorman’s expected profit if they follow the strategy described in parts d and e?

g) What is the increase in expected profit that Gorman can attain if they acquire and utilize the results of the test market study? (HINT: This is EVSI)

h)    What is the value of EVPI? Explain what this number means in the context of this problem

Answer 1

a) P(Low/favorable) = P(favorable/low)*P(low)/ [ P(favorable/low)*P(low)+P(favorable/medium)*P(medium)+P(favorable/high)*P(high)] = 0.40*0.10/[0.4*0.1+0.35*0.40+0.25*0.6]=0.1212

b)P( Medium/favorable)= 0.40*0.35/[0.4*0.1+0.35*0.40+0.25*0.6]=0.4242

c) P( High/favorable) = 0.60*0.25/[0.4*0.1+0.35*0.40+0.25*0.6]=0.4545

d) E( Manufacture) = -20*0.1212 +40*0.4242+100*0.4545=60

E( Purchase) = 10*0.1212 +45*0.4242+70*0.4545=52.116

He should manufacture the component.

Please repost the other parts individually