Tickets for the gala Opening Night festivities in Oklahoma City are available for $80 in advance at a couple of area businesses
If you wait until you arrive at the venue, you will pay full face value of $100 per ticket to enjoy the same festivities. If you buy a ticket and don't use it, you can buy $25 worth of chemicals and treat the ticket so that it can be used the following year. You have been taking orders from your friends for a few years and historically demand has been normally distributed with a mean of 50 tickets and a standard deviation of 10. What's the best quantity of tickets to purchase for this year's event?
What will be an ideal response?
Answer: The shortage cost is $20 (pay $100 on the day versus $80 beforehand) and the excess cost is just $5 (the $80 ticket can be doctored using $25 of chemicals for a total cost of $105 versus paying $100 the next year). The target service level is 20/25 = 0.8 and the z-score is 0.8416. The order quantity is .
Another popular answer is that the cost of excess is $25 (for the chemicals) based on the possibility of paying $80 in advance the next year versus $100 the night of the event. In this case the target service level is 0.4444 and the z-score is -0.1397 for an order quantity of . Since the base price of the ticket is $100, the 58.4 answer is preferred.
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