Question

The Getz Products Company is investigating the possibility of producing and marketing backyard storage sheds. Undertaking this project would require the construction of either a large or small manufacturing plant. The market for the product produced – storage sheds - could be either favorable or unfavorable. Getz, of course, has the option of not developing the product at all.

With a favorable market, a large facility would give Getz a net profit of $200,000. If the market is unfavorable, a $180,000 net loss would occur. A small plant would result in a net profit of $100,000 in a favorable market, but a net loss of $20,000 would be encountered if the market was unfavorable.

Getz Products’ POM manager believes that the probability of a favorable market is the same as that of an unfavorable market (.50/.50)

Suppose that Getz could have their marketing department perform a survey at a cost of $10,000. Getz would then use the results of the survey to decide whether to build a large plant or a small plant, or not to build at all

If the company decides not to conduct the survey, the probabilities and payoffs given previously apply.

If the company decides to conduct the survey, it will result in either a favorable or unfavorable forecast.

If the forecast is favorable, the probability of the market actually being favorable is 0.78, the probability of the market being unfavorable is 0.22. If a large plant is then built, the final result would be a net profit of $190,000 with a favorable market and a net loss of $190,000 with an unfavorable market. If a small plant is built, the final result would be a net profit of $90,000 with a favorable market and a net loss of $30,000 with an unfavorable market. If no plant is built the net loss will be $10,000 (the cost of the forecast survey).

If the forecast is unfavorable, the probability of the market actually being favorable is 0.27, the probability of the market being unfavorable is 0.73. The final results would be the same as above: if a large plant is then built, the final result would be a net profit of $190,000 with a favorable market and a net loss of $190,000 with an unfavorable market. If a small plant is built, the final result would be a net profit of $90,000 with a favorable market and a net loss of $30,000 with an unfavorable market. If no plant is built the net loss will be $10,000 (the cost of the forecast survey).

We estimate the probability of a favorable survey to be 0.45 and the probability of an unfavorable survey to be 0.55.

Draw and Solve a Decision Tree to determine the best plan for Getz.

Answer 1

Let we draw a Decision Tree is as follows

Let we calculate Profit if Getz conduct or not conduct survey as

If Getz not conduct Survey then

Profit ( Large Plant) = 0.5*200000 - 0.5*180000 = 100000 -  90000 = $10000

Profit (Small Plant) = 0.5*100000 - 0.5*20000 = 50000 - 10000 = $40000

That is If Getz not conduct survey then Total profit including Large and Small plant is $50000 .............(1)

If Getz conduct Survey then

Profit ( Large Plant) = (0.45*0.78*190000 + 0.55*0.27*190000) - (0.45*0.22*190000 + 0.55*0.73*190000) = (66690 + 28215) - (18810 + 76285) = -$190

Profit (Small Plant) = (0.45*0.78*90000 + 0.55*0.27*90000) - (0.45*0.22*30000 + 0.55*0.73*30000) = (31590 + 13365) - (2970 + 12045) = $29940

Profit (No plant Build) = (0 + 0) - (0.45*0.22*10000 + 0.55*0.73*10000) = 0 - (990 + 4015) = -$5005

That is If Getz conduct survey then Total profit including Large and Small plant and no plant build is $24745 ........................................(2)

From (1) and (2) we see that Getz get more profit if not conduct the survey according conducting survey.