On consecutive Sundays, Mac, the owner of a local newsstand, purchases a number of copies of The Computer Journal, a popular weekly magazine. He pays 25 cents for each copy and sells each for 75 cents. Copies he has not sold during the week can be returned to his supplier for 10 cents each. From past experience, we saw that the weekly demand for the Journal is approximately normally distributed with mean μ = 11.73 and standard deviation σ = 4.74. Because Mac purchases the magazines for 25 cents and can salvage unsold copies for 10 cents, his overage cost is co = 25 – 10 = 15 cents. His underage cost is the profit on each sale, so that cu = 75 – 25 = 50 cents. The critical ratio is cu/(co + cu) = .77. Hence, he should purchase enough copies to satisfy all the weekly demand with probability .77. The optimal Q* is the 77th percentile of the demand distribution. Using Table A-4, we obtain a standardized value of z = 0.74. The optimal Q is Q* = σz + μ ≈ 15.
Compute the expected number of newspapers sold and the expected profit using the formulas from the Newsvendor model.