# End of Season Discount for Teddy Bower for Optimal Order Quantity

Question

A large outdoor clothing retailer, Teddy Bower, has decided to sell animal-print hunting boots in the coming spring season. Teddy Bower has contacted several Taiwanese suppliers, and £40 per pair of boots is the best quote that Teddy Bower get so far. Teddy Bower anticipates this fashionable animal-print design will fade off soon, thus the animal-print hunting boots will only be sold for one season. Given the short life cycles of such products and the long lead time quoted by the Taiwanese supplier, Teddy Bower has only one opportunity to place an order with its supplier prior to the beginning of spring season. Due to competition, Teddy Bower has decided to sell these boots at £54 per pair. In addition, Teddy Bower anticipates excess inventory will be sold off at a 50 percent discount at the end of the season. Teddy Bower’s demand forecast for the coming spring season is normally distributed with a mean of 400 pairs and a standard deviation of 150 pairs.

What are the under-and over-stocking cost of a pair of boots for Teddy Bower? Assume no transportation cost, inventory cost or any other additional cost for Teddy Bower to purchase the boots from its supplier except the whole-sale price £40 per pair.

Under-stocking cost

Over-stocking cost

If Teddy Bower decides to include these boots in its assortment, how many boots should it order from its supplier?

Suppose that Teddy Bower anticipates the excess inventory might be sold off at a different discount rather than 50% off. What would be the alternative end-of-season discount that would lead to optimal order quantity of 450 pairs?

Summary

This question belongs to economics and discusses about end of season discount that would lead to optimal order for Teddy Bower clothing company.

Word count: NA

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