1. A chemical company is building a plant to market Zircag, a new chemical used primarily in agriculture. The firm is uncertain about the demand for Zircag during the initial year of sales. However, the following probability distribution was assessed.
Demand for Zircag for Initial Year (kilograms)
Zircag is produced on a special-purpose machine. Each such machine has a yield of 200 kilograms of Zircag per year. The fixed cost of purchasing and operating one machine is $560,000 per year, which includes supervision, maintenance, and other fixed charges, plus annualized interest and equipment costs. Suppose the profit from one year's production of one machine (but not covering the fixed costs) is $1.3 million, assuming demand is sufficient to run the machine for the entire year.
The problem facing the chemical company is to decide how many machines to install in the plant for the first year. The second and subsequent years pose little problem, because the firm is able to buy additional machines if needed, and any unused capacity can be absorbed in future years as sales grow.
a) How many machines should the firm install to maximize expected net profit in the first year?
b) What is the EMV of this action?
c) What would be the expected value of perfect information for this problem?
d) What is the company's risk profile if they take your recommended action?
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This posting determines expected value of perfect information and other factors.