Question

It costs a pharmaceutical company $75,000 to produce a 1,000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for $125 per pound and leftover amounts of the drug can be sold for $30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.

Answer 1

	Best Case	Most Likely	Worst Case
Total Cost of Drug/Batch	75000	75000	75000
Pounds Produced /Batch	900	850	700
Annual Demand in pounds	20000	17500	10000
Sales Price per pound	125	125	125
Sales Price of Leftover Drug per pound	30	30	30
Batches to be produced	22	20	14
Cost of Batches	1650000	1500000	1050000
Sales from Drug Batches	2475000	2125000	1225000
Sales from Drug Leftover	0	0	0
Total Sales	2475000	2125000	1225000
Profit	825000	625000	175000

The number of batches to be produced in each scenario to have maximum profit is given in the table..

Therefore, in best scenario, 22 batches should be produced to maximize profit

in Most likely scenario, 20 batches should be produced to maximize profit

in best scenario, 22 batches should be produced to maximize profit

in worst scenario, 14 batches should be produced to maximize profit.

Hope I answered your query..