The Sunshine Manufacturing Company Has Developed a Unique New Product

The Sunshine Manufacturing Company has developed a unique new product and must now decide between two facility plans.The first alternative is to build a large new facility immediately.The second alternative is to build a small plant initially and to consider expanding it to a larger facility three years later if the market has proven favorable.
Marketing has provided the following probability estimates for a ten-year plan: $$\begin{array} { c c c } \hline \hline \text { First 3-Year Demand } & \text { Next 7-Year Demand } & \text { Frobability } \\\hline \text { Unfavorable } & \text { Unfavorable } & .2 \\\text { Unfavorable } & \text { Favorable } & .0 \\\text { Favorable } & \text { Favorable } & .7 \\\text { Favorable } & \text { Unfavorable } & .1 \\\hline \hline\end{array}$$ If the small plant is expanded,the probability of demands over the remaining seven years is 7/8 for favorable and 1/8 for unfavorable.The accounting department has provided the payoff for each outcome: $$\begin{array} { l c r } \hline \hline{ \text { Demand } } & \text { Facility Plan } & \text { Payoff } \\\hline \text { Favorable, favorable } & 1 & \$ 5,000,000 \\\text { Favorable, unfavorable } & 1 & 2,500,000 \\\text { Unfavorable, unfavorable } & 1 & 1,000,000 \\\text { Favorable, favorable } & \text { 2--expanded } & 4,000,000 \\\text { Favorable, unfavorable } & \text { 2-expanded } & 100,000 \\\text { Favorable, favorable } & \text { 2-not expanded } & 1,500,000 \\\text { Favorable, unfavorable } & \text { 2--not expanded } & 500,000 \\\text { Unfavorable, unfavorable } & \text { 2-not expanded } & 300,000 \\\hline \hline\end{array}$$ With these estimates,analyze Sunshine's facility decision and:
a. Perform a complete decision tree analysis.
b. Recommend a strategy to Sunshine.
c. Determine what payoffs will result from your recommendation.