A small market orders copies of a certain magazine for its magazine rack each we

Question

A small market orders copies of a certain magazine for its magazine rack each week. Let random variable X equal to demand for the magazine, with a probability mass function shown below. Suppose the store owner actually pays $2.00 for each copy of the magazine and the price to customers is $3.00. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? [Hint: For both three and four copies ordered, express net revenue as a function of demand X, and then compute the expected revenue.]

P(X) |1/15 2/15 3/15 4/15 3/15 2/15 Ans:

Explanation / Answer

For,

X = 3,

Expected net revenue = (-1 * 1/15) + (4*2/15) + (9 * 3/15)

= 34 /15

For,

X = 4,

Expected net revenue = (-3 * 1/15) + (2*2/15) + (7 * 3/15) + (12 * 4/15)

= 70/15

Hence, it is profitable to order 4 copies instead of 3.

Hope this helps.

Ordered = 3 Copies Sold 1 2 3 4 5 6 Profit 3 6 9 Loss -4 -2 0 Net -1 4 9 Ordered = 4 Copies Sold 1 2 3 4 5 6 Profit 3 6 9 12 Loss -6 -4 -2 0 Net -3 2 7 12

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