A toy company has developed a new toy for the upcoming Christmas season. Since this toy is considerably different from the ones it has manufactured previously, the company will need to develop a new production facility for it. Three facility sizes - small, medium and large - are under consideration. Given the nature of the toy market, the company is unsure as to what demand level it will encounter. The preliminary analysis is to be based on the demand being low, average, or high. The accompanying table shows the estimated profits, in $1,000's, of the various facility-size demand combinations. These estimated profit amounts factor in the cost of the operation as well as the time value of money.

Demand Level

Facility Size	Low	Average	High
Small	$750	$900	$900
Medium	$350	$1,100	$1,300
Large	-$250	$1,000	$4,000

The company's initial assessment of the probabilities of the different market sizes is:

• probability of low = 0.5
• probability of average = 0.3
• probability of high = 0.2a) Draw the decision tree that would help in this analysis. Be sure to indicate all probabilities and payoffs. b) Based on an expected value analysis, what is your recommendation for the facility size that the company should select? Why? c) Now, consider only the large and medium facility sizes. Keeping all other variables and values the same as in the problem, what would the profit for the medium facility under the Low Demand scenario need to be so that the expected profit of these two options (small and medium) are equal?