What is optimal number of trees for this merchant to order

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Reference no: EM131296402

A merchant is considering how many Christmas trees he should purchase. Because of the shortness of the season, only one order can be placed and that order must be placed well before the Christmas season begins. The merchant plans to be open for a total of 26 days before Christmas. The trees cost the merchant $22.50 each and they can be sold for $54.99 apiece. They have no salvage value, but any unsold trees must be disposed of at a cost of $6.00 per tree. The seasonal sales license required by the city to sell trees in the city is $250 and rental of the parking lot space for the tree lot be $500. The merchant will have to hire two assistants who will work an average of 8 hours per day at a cost to the merchant of $15.50 per hour. Demand over the past seasons indicates that a good way to model the quantity demanded at $55 per tree is by using a normal distribution with a mean of 480 trees and a standard deviation of 67 trees with no fewer than 3400 trees being sold in any event. What is the optimal number of trees for this merchant to order? What will be the expected profit?

Reference no: EM131296402

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