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It costs a pharmaceutical company $75,000 to produce a 1,000-pound batch of a drug. The average...

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Basic Math

It costs a pharmaceutical company $75,000 to produce a1,000-pound batch of a drug. The average yield from a batch isunknown but the best case is 90% yield (that is, 900 pounds of gooddrug will be produced), the most likely case is 85% yield, and theworst case is 70% yield. The annual demand for the drug is unknown,with the best case being 20,000 pounds, the most likely case 17,500pounds, and the worst case 10,000 pounds. The drug sells for $125per pound and leftover amounts of the drug can be sold for $30 perpound. To maximize annual expected profit, how many batches of thedrug should the company produce? You can assume that it willproduce the batches only once, before demand for the drugis known.

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4.1 Ratings (562 Votes)

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..
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