The production supervisor of a small pharmaceutical firm has observed a decreasing demand for potassium regurgitol (PRG) over a two-month period, and since the plant manager has been throwing up the low sales of this product at the weekly staff meetings, the supervisor decides to discontinue its production immediately. On the day of this decision, the inventory of PRO is 18,000 kg. Based on the orders on hand, the manager projects the following weekly demand for the next six weeks:

(a) Use a semi log plot of the projected demand figures to derive an equation for D as a function of ((weeks) from the present time.

(b) Write a differential balance on the inventory I (kg) of PRG, and integrate it to determine I as a function of t.

(c) If the demand continues to follow the projected trend of the next six weeks, how much PRG will eventually have to bediscarded?

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Week 1 2 Demand D(kg/wk) 2385 1890 3 4 5 6 1506 1196 950 755