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 $5400, making Digitalis a profit of $594. 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 a 13% chance that it is defective and an 87% chance that it is not defective.
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.
in the long run, they should except to make __ dollars on each processor sold
B. Digitalis can expect to lose money from selling these processors.
in the long run, they should except to lose __ dollars on each processor sold
C. Digitalis should expect to neither make nor lose money from selling these processors.
In the long run, they should expect to neither make nor lose money on each processor sold.
To determine whether Digitalis can expect to make or lose money from selling the processors, we need to calculate the expected value of the profit earned per processor sold and the expected value of the amount refunded due to defective processors.
Let's calculate the expected value of the profit earned per processor sold:
Profit per processor = Revenue per processor - Cost per processor
Given that the revenue per processor is $5400 and the profit is $594, we can find the cost per processor:
Cost per processor = Revenue per processor - Profit per processor
Cost per processor = $5400 - $594 = $4806
Now, let's calculate the expected value of the profit earned per processor sold:
Expected profit earned per processor sold = Probability of a non-defective processor * Profit per processor
Expected profit earned per processor sold = 0.87 * $594 = $516.18
Next, let's calculate the expected value of the amount refunded due to defective processors:
Expected refund amount per processor sold = Probability of a defective processor * Cost per processor
Expected refund amount per processor sold = 0.13 * $4806 = $624.78
Finally, let's calculate the overall expected value:
Expected value = Expected profit earned per processor sold - Expected refund amount per processor sold
Expected value = $516.18 - $624.78 = -$108.60
Since the overall expected value is negative, Digitalis can expect to lose money from selling these processors.
Therefore, the answer is B. Digitalis can expect to lose $108.60 on each processor sold.
To determine whether Digitalis can expect to make or lose money from selling the luteA processors, we need to calculate the expected profit per processor sold.
First, let's calculate the profit earned on each non-defective processor. The selling price is given as $5400, and the profit is given as $594. Therefore, the profit per non-defective processor is $594.
Next, let's calculate the expected refund amount per defective processor. The probability of a processor being defective is 13%, so the refund amount will be the full selling price of $5400. Therefore, the expected refund amount per defective processor is $5400 * 13% = $702.
To calculate the overall expected profit per processor sold, we need to consider the probabilities of a processor being defective (13%) and not defective (87%). The expected profit per processor sold is calculated as follows:
Expected profit per processor sold = (probability of being non-defective * profit per non-defective processor) +
(probability of being defective * expected refund per defective processor)
= (87% * $594) + (13% * $702)
= $516.78 + $91.26
= $608.04
Therefore, the answer is:
A. Digitalis can expect to make money from selling these processors.
In the long run, they should expect to make $608.04 dollars on each processor sold.