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? What is the expected profit if three magazines are ordered? $ What is the expected profit If four magazines are ordered? $ How many magazines should the store owner order? 3 magazines 4 magazines

Explanation / Answer

Net revenue is expressed as R(x)=Profit per unit*number of units sold. Since, price paid by owner is $2 and price to customer is $4, therefore, profit per magazine is $2 [$4-$2]. Thus, for 1 magazine sold, the revenue is $2*1=$2, for two magazines, revenue is $4 and so on. therefore, multiplying each value of a random variable by a constant (here 2) multiplies the mean by that constant. That is E(aX)=aE(X).

Thus, The expected profit for ordering 3 magazines is E(2X)=2E(X)=2*sigma x*p(x)=2[1*2/17+2*1/17+3*5/17]=$2.24

Expected profit for ordering 4 magazines is 2[1*2/17+2*1/17+3*5/17+4*3/17]=$3.65

Thus, store owner should order 4 magazines ($3.65>$2.24).

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