An airport magazine store has to determine the appropriate number of copies of a weekly magazine to order. Depending on the cover story, demand for the magazine varies. Historical records suggest that the probability distributions of weekly demand is as follows: Number of magazines 70 75 80 85
Probability 0.35 0.25 0.20 0.20
The store purchases the magazines for $1.25 and sells them for $2.50. Any copies left over at the end of the week are donated to local charity. Let D be the weekly demand and Q be the order size.
If D > Q, then the store has sold all that was purchased and realized a net profit of $ 2.50 Q – 1.25 Q.
If D < Q, then the store has (Q-D) copies left over. D copies are sold at $2.50 and the remainder is donated. Thus, the net profit is $ 2.50 D – 1.25 Q.
To demonstrate the simulation process, develop 3 simulation runs, using random numbers (RN) given in the following table. These random numbers have been drawn randomly from a bag containing numbers from 00 to 99. For each order quantity Q (70, 75, 80, and 85), compute the weekly profit for the 3 runs and then compute the average profit for each order size to determine the best order size.
Run # RN D Profit
Q= 70 Q = 75 Q = 80 Q = 85
1 48
2 12
3 77
Average Profit
Based on the average profit, what is the best order size Q?