A manufacturer of electronic calculators offers a one-year warranty. If the calculator fails for any reason during this period, it is replaced. The time to failure is well modeled by the following probability distribution: f(x) = 0.125e^-0.125x x > 0
(a) What percentage of the calculators will fail within the warranty period?
(b) The manufacturing cost of a calculator is $50, and the profit per sale is $25. What is the effect of warranty replacement on profit?

(a) 11.75%

(b) Profit decreases by $5.88 per calculator.

Step-by-step explanation:

(a) The percentage of failures with time is given by the following expression:

Integrating this function from x = 0 to x = 1 year, gives us the percentage of failures in the first year:

11.75% of the calculators will fail within the warranty period.

(b) If the cost of a calculator is $50, and the profit per sale is $25, the average revenue per calculator is $75. Considering no income in failed calculators, the new cost per calculator is:

The effect of warranty replacement on profit is given by the difference in cost per calculator:

Profit decreases by $5.88 per calculator.

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