Question

Problem 4

The marketing manager of a food products company is attempting to decide whether they should introduce a new line of salad dressings. The company can test market the salad dressings in selected geographic areas or bypass the test market and introduce the product nationally. The cost of the test market is $135,000. If the company conducts the test market, it must wait to see the results before deciding whether to introduce the salad dressings nationally. The probability of a positive test market result is estimated to be 0.6. Alternatively, the company can decide not to conduct the test market and go ahead and make the decision to introduce the dressings or not. If the salad dressings are introduced nationally and are a success, the company estimates that it will realize an annual profit of $1,500,000 while if the dressings fail it will incur a loss of $600,000. The company believes the probability of success for the salad dressings is 0.50 if they are introduced without the test market. If the company does conduct the test market and it is positive, then the probability of successfully introducing the salad dressings increases to 0.7. If the test market is negative and the company introduces the salad dressings anyway, the probability of success drops to 0.30.

1. Draw a complete decision tree for this problem. Clearly present all decision and event nodes, probabilities, and payoffs.
2. What should the management do to achieve the highest expected payoff?

Answer 1

a)

Decision tree is following:

Decision nodes are square boxes

and event nodes are round boxes

b)

Expected Monetary Value (EMV) of each of the nodes are computed as follows:

EMV of node 6 = .7*1500000+.3*(-600000)-135000 = 870000-135000 = $ 735,000

EMV of node 7 = $ -135,000

EMV of node 4 = MAX(EMV of node 6, EMV of node 7) = 735,000

EMV of node 8 = .3*1500000+.7*(-600000)-135000 = 30000-135000 = $ -105,000

EMV of node 9 = $ -135,000

EMV of node 5 = MAX(EMV of node 8, EMV of node 9) = -105,000

EMV of node 2 = .6*EMV of node 4 + 0.4*EMV of node 5

= 0.6*735000+0.4*(-105000)

= $ 399,000 (in the decision tree, this is shown as 534,000-135,000 = 399,000)

EMV of node 3 = 0.5*1500000+0.5*(-600000)

= $ 450,000

EMV of node 3 is maximum.

Therefore, management should bypass the test market and introduce the product nationally.