Chemcon has taken over the production of Nasacure from a rival drug company. Chemcon must build a plant to produce Nasacure by the beginning of 2007. After the plant is built, the plant’s capacity...

Chemcon has taken over the production of Nasacure from a rival drug company. Chemcon must build a plant to produce Nasacure by the beginning of 2007. After the plant is built, the plant’s capacity cannot be changed. Each unit sold brings in $10 in revenue. The fixed cost (in dollars) of producing a plant that can produce x units per year of the drug is 5,000,000 +10x. This cost is assumed to be incurred at the end of 2007. In fact, we assume that all cost and sales cash flows are incurred at the ends of the respective years. If a plant of capacity x is built, the variable cost of producing a unit of Nasacure is 6 - 0.1(x - 1,000,000)/100,000. For example, a plant capacity of 1,100,000 units has a variable cost of $5.90. Each year, a plant operating cost of $1 per unit of capacity is also incurred. Based on a forecasting sales model from the previous 10 years, Chemcon forecasts that demand in year t, D_t
, is related to the demand in the previous year, D_t–1, by the equation




where e_t
is a random term that is normally distributed with mean 0 and standard deviation 29,320. The demand in 2006 was 1,011,000 units. If demand for a year exceeds production capacity, all demand in excess of plant capacity is lost. Chemcon wants to determine a capacity level that will maximize expected discounted profits (using a discount rate of 10%) for the time period 2007 to 2016. Use simulation to help it do so.