Using decision analysis methods to aggregate them into a decision tree

You are the director of marketing for a fast food chain and you are considering

introducing a new type of sandwich for purchase. You feel that the demand

will be either low or high with respective probabilities P (low) = .40 and

P (high) = .60.

Before making a decision on whether to sell the sandwich or not, you

are considering using a consumer panel of two people to sample the product.

Each person independently decides whether they would buy the sandwich on

a regular basis. Notice, then, that if we conduct this test, either 0, 1 or 2 of

the representative consumers would buy the product regularly. That is, if we

conduct the test, the potential outcomes are "0 Buy", "1 Buy" or "2 Buy". If

demand is low, then the probability that 0 buy is 64%, the probability that 1

buys is 32% and the probability that 2 buy is 4%. If demand is high, then the

probability that 0 buy is 36%, the probability that 1 buys is 48% and the

probability that 2 buy is 16%.

In terms of profitability, if demand is low, we lose $1,000. If demand is high

we make $2,000. The cost of conducting the test with the two consumers is

$50.

Order the decisions and uncertainties you face in this decision problem and

aggregate them into a decision tree. After labeling both the endpoint values in

terms of profitability and the probabilities within the tree, perform backwards

induction to determine the optimal strategy. Assume you are an expected

value decision maker.