Construct a decision tree for the information in the payoff table assuming that the prior probabilities of low, moderate, and high demands are, respectively, .3, .5, and .2.

The example involves a capacity-planning problem in which a company must choose to build a small, medium, or large production facility. The payoff obtained will depend on whether future demand is low, moderate, or high, and the payoffs are as given in the first table.

Possible Future Demand Alternatives Small facility Moderate High $10 Low $10* $10 12 Medium facility 12 2 Large facility -4 16