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 X = demand for the magazine, with the following pmf.

4/15

Suppose the store owner actually pays $2.00 for each copy of the magazine and the price to customers is $4.00. 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.]

(a) What is the expected profit if three magazines are ordered? (Round your answer to two decimal places.)

(b) What is the expected profit if four magazines are ordered? (Round your answer to two decimal places.)

x 1 2 3 4 5 6 p(x)        1/15    1/15

4/15

   4/15    2/15    3/15

Explanation / Answer

selling price = 4

cost price = 2

profit = 4-2 = 2

now

E(X) = X1*P(X1)+X2*P(X2)+....+XN*P(XN)

E(X) = 3*P(3) = 3*4/15 = 4/5 = 0.8

PROFIT = 0.8*2 = 1.6

B) E(4) = 4*4/15 = 16/15 = 1.06

PROFIT = 2*1.06 = 2.12

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