Simulating Rupert’s Profits
Rupert sells daily newspapers on a street corner. Each morning he must buy the same fixed number q of
copies from the printer at c = 55 cents each, and sells them for r = $1.00 each through the day. He’s
noticed that demand D during a day is close to being a random variable X that’s normally distributed
with mean of 135.7 and standard deviation of 27.1, except that D must be a nonnegative integer to
make sense, so D = max(X,0) where . rounds to the nearest integer (Repurt’s not your average news
vendor). Further, demands form day to day are independent of each other. Now if demand D in a day is
no more than q, he can satisfy all customers and will have q – D
0 papers left over, which he sells as
scrap to the recycler on the next corner at the end of the day for s = 3 cents each (after all, it’s old news
at that point). But if D > q, he sells out all of his supply of q and just misses those D –q > 0 sales. Each day
starts afresh, independent of any other day, so this is a single-period problem, and for a given day is
static model since it doesn’t matter when individual customers show up the day. Develop a spreadsheet
model to simulate Rupert’s profits for 30 days, and analyze the result.