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.

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.]

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

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)        1/12    1/12 3/12    3/12    2/12    2/12

Explanation / Answer

a)Let the profit be y, the demand for magazine be x, and the number of magazines ordered be m, then we get,

y = 4*x - 2*m for m >x
y = 2m for m <=x

b) When order three copies;

h(x)   -2     2       6       6       6      6
p(x) 1/12 1/12 3/12 3/12 2/12 2/12

where h(x) is the profit selling x copies.

E(X3) = (-2*1/12) + (2*1/12) + (6*3/12) + (6*3/12) + (6*2/12) + (6*2/12) = 5

c) When order four copies:

h(x)   -4       0        4        8       8         8
p(x) 1/12   1/12   3/12   3/12   2/12   2/12

E(X4) = (-4*1/12) + (0*1/12) + (4*3/12) + (8*3/12) + (8*2/12) + (8*2/12) = 5.33

Order four copies

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