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# Description of Optimal Order Quantity

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The bookstore at a university purchases sweatshirts emblazoned with the school name and logo from a vendor. The vendor sells the sweatshirts to the store for \$38 apiece. The cost to the bookstore for placing an order is \$120 and the carrying cost is 25% of the average annual inventory value. The bookstore manager estimates that 1,700 sweatshirts will be sold during the year. The vendor has offered the bookstore the following volume discount schedule.

Determine the bookstore's optimal order quantity given the above quantity discount information.

https://brainmass.com/math/optimization/description-of-optimal-order-quantity-350949

#### Solution Preview

First calculate economic order quantity

EOQ = As??2 x 1700 x 120/(\$38 x 0.25) = 207.23

Calculate carrying and ordering costs:

Carrying costs: 207.23/2 x 9.50 = \$984.34
Ordering costs: 1700/207.23 x 120 =\$984.41
Total carrying ordering costs ...

#### Solution Summary

Determine the bookstore's optimal order quantity given the above quantity discount information.

\$2.19