Question

Digitalis is a technology company that makes high-end computer processors. Their newest processor, the luteA, is going to be sold directly to the public. The processor is to be sold for $3900, making Digitalis a profit of $547. Unfortunately there was a manufacturing flaw, and some of these luteA processors are defective and cannot be repaired. On these defective processors, Digitalis is going to give the customer a full refund. Suppose that for each luteA there is an 11% chance that it is defective and an 89% chance that it is not defective. (If necessary, consult a list of formulas.)

If Digitalis knows it will sell many of these processors, should it expect to make or lose money from selling them? How much?
To answer, take into account the profit earned on each processor and the expected value of the amount refunded due to the processor being defective.
a. Digitalis can expect to make money from selling these processors.
b. In the long run, they should expect to make ? dollars on each processor sold.
c. Digitalis can expect to lose money from selling these processors.
d. In the long run, they should expect to lose ? dollars on each processor sold.
e. Digitalis should expect to neither make nor lose money from selling these processors.

Answer 1

a. Digitalis can expect to make money from selling these processors.

A profit of $118

Explanation:

Chance of processor being defective = 11%

Chance that processor isn't defective = 89%

Sales price of processor = $3900

Profit made = $547

Full refund is given for a defective processor ; this means loss of manufacturing or production cost : Sale price - Profit ; $3900 - $547 = $3353

89% of profit - 11% of production cost

0.89*547 - 0.11 * 3353

486.83 - 368.83

= $118

This means a profit of $118