question archive Tom is contemplating the upcoming purchasing decisions for a local supermarket
Tom is contemplating the upcoming purchasing decisions for a local supermarket
Subject:ManagementPrice:3.87 Bought7
Tom is contemplating the upcoming purchasing decisions for a local supermarket. Specifically, he is considering the order quantity for Thanksgiving turkey cooking kits. Naturally, the kit will only sell during the week leading up to Thanksgiving. It costs the supermarket $6.00 per kit to procure, and they sell it for $12.00 per kit. Any unsold kit by Thanksgiving is sold to a liquidator for $2.00 per kit. He only has one opportunity to purchase this kind of kits and cannot predict demand for the kits with certainty. Data from previous years suggest that demand is well described by a normal distribution with mean value 60 and standard deviation 10.
Tom is contemplating the upcoming purchasing decisions for a local supermarket. Specifically, he is considering the order quantity for Thanksgiving turkey cooking kits. Naturally, the kit will only sell during the week leading up to Thanksgiving. It costs the supermarket $6.00 per kit to procure, and they sell it for $12.00 per kit. Any unsold kit by Thanksgiving is sold to a liquidator for $2.00 per kit. He only has one opportunity to purchase this kind of kits and cannot predict demand for the kits with certainty. Data from previous years suggest that demand is well described by a normal distribution with mean value 60 and standard deviation 10.
a. How many baking kits should Tom purchase to maximize the expected profit of the supermarket?
b. Suppose the liquidator no longer buys any kit. If there is unsold kit, Tom can give you as a gift. To ensure there is no more than a 1 in 100 chance he will sell out all the kits, how many kits will you suggest Tom to purchase?
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Solution:
(a) Cu = 12 – 6 = 6
Co = 6 – 2 = 4
The critical ratio = 6 / (6+ 4) = 0.6
Use standard normal distribution table, z = 0.2533 Q = 60 + 0.2533 * 10 = 62.533
So the number of kits should be 63
(b) In this case, the service level is 1 - 1/100 = 0.99 Use standard normal distribution table, z = 2.33 Q = 60 + 2.33 * 10 = 83.3
So the number of kits should be 84
