Based on a demand analysis forecast, a factory plans to produce 80,000 video game cartridges this quarter, on average, with an estimated uncertainty of 25,000 cartridges as the standard deviation. The fixed costs for this equipment are $72,000 per quarter, and the variable cost is $1.43 per cartridge produced.
a. What is the forecast expected total cost of the cartridges produced?
b. What is the uncertainty involved in this forecast of total cost, expressed as a standard deviation?
c. Find the coefficient of variation for the number of cartridges produced and for the total cost. Write a paragraph interpreting and comparing these coefficients of variation.
d. After the quarter is over, you find that the factory actually produced 100,000 cartridges. How many standard deviations above or below the average is this figure?
e. Suppose the firm actually produces 200,000 cartridges. How many standard deviations above or below the average is this figure? Would this be a surprise in light of the earlier forecast? Why or why not?