The Plastic Production Company needs to expand its production capacity. This can be done in one of two ways: using overtime in its current plant or leasing another plant. Overtime has a cost penalty (above regular time) of $3 per case of product produced, and can only be used for up to 15,000 cases per year. Leasing another plant would entail an annual fixed leasing cost of $25,000. however, the work force of this plant would be paid on a regular-time basis and could produce any number of cases up to a maximum of 20,000 cases annually. The company estimates that additional demand (beyond what can be produced in its current plant in regular time) may take on the following values, with corresponding probabilities: Additional Demand (cases per year) 5,000 10,000 15.000 Probabilities 0.3 0.5 0.2 a. Draw a decision tree for this problem, and find the optimal decision to minimize expected cost. b. Suppose a market research company offers to perform a survey to determine the exact quantity of additional demand that will be forthcoming. Should the company be willing to pay $1,000 for such a perfect survey? Why or why not? (Use EVPI to justify your answer) c. What is the expected opportunity loss (EOL) of the best decision in (a)?