5. A small shop orders copies of a certain magazine each week. Let A\' = demand

Question

5. A small shop orders copies of a certain magazine each week. Let A' = demand for the magazine with pmf The shop owner pays $ 1.80 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 one. two. three or four copies of the magazine ? Hint: Introduce random variables: Vk = the number of magazines sold if k magazines are ordered. Rk = the net profit if k magazines are ordered, k = 1,2,3,4 and find their probability distributions.

Explanation / Answer

to find the expected gain, we have to find a probability of each outcome and multiply it with profits ( 1.2 in this case) R(k=1)= 0.3*1 *3 -0.3*1*1.8 =0.3*1(3-1.8)=0.3*1*1.2=0.36 R(k=2)= 0.4*2*1.2=0.96 R(k=3)=0.2*3*1.2=0.72 R(k=4)=0.1*4*1.2=0.48 So a seller would be profitable if he sells 2 magazines per week.

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