Suppose SuperWidget is the latest and greatest product that you are thinking of manufacturing. You think the SuperWidget is worth making, but your not sure just how sales will go. Your biggest question is how much of a market there will actually be for selling the SuperWidget. The decision you have to make is if you should go Big Time manufacturing and marketing or only Small Scale manufacturing and marketing.

The cost of going Big Time is computed to be $459,300. The Small Scale plan will cost $81,600. An assessment of the descriptive and predictive analytics available, you assign a prior probability of 0.43 to the existence of a Huge Market for SuperWidget with the only alternative to this being a Limited Market with probability 0.57.

The available analytics also lead you to estimate the income of the Huge Market to be $935,500 if you go Big Time and $390,600 if you go Small Scale, whereas the estimated income for the Limited Market would be $202,100 for the Small Scale plan and $215,000 for the Big Time plan.

Another decision you must make is whether or not to conduct a market research study to assess the market potential for SuperWidget. The market research will cost $12,530. The history of your market research has shown that when there is a huge market for a product like SuperWidget, the market research correctly predicts this with probability 0.77. However, if there is a limited market for a product like this the market research has a 0.93 probability of predicting this correctly.

State the probabilities (to 3 decimal places).

1. P (Huge Market | market research predicts Huge Market)?

2. P (Huge Market | market research predicts Limited Market)?

3. Find the marginal probability that the market research predicts Limited Market.

4. Construct and solve the decision tree for this problem to maximize your profit, highlighting the best choices