### Inventory with shortage of stock allowance

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Evaluation of EOQ - Inventory with shortage of stock allowance

The bookstore at Smith College purchases sport shirts with the college logo to sell from a local vendor.   The vendor sells the sport shirts to the college for \$38 each.  The cost to the bookstore for placing each order is \$120.  The carrying cost is \$5.20 per shirt per year.   The bookstore estimates that 1700 sport shirts will be sold over the next year and does not want any shortages.  The bookstore sells the shirt for \$50 each.   There are 260 business days a year for the bookstore.   Lead time for filling an order once placed is 2 weeks.   The vendor has offered the College Bookstore the following discounts:

 Order Size Discount % of Order Cost of Shirts from Vendor 1-299 0% discount \$38 300-499 2% discount \$37.24 500-799 4% discount \$36.48 800+ 6% discount \$35.72

Assuming the local vendor eliminates it's discounts and charges a flat rate of \$35 per shirt.  The bookstore is considering allowing backorders if it is profitable to do so.  They determine their shortage cost per shirt to be \$7.50.  Should the bookstore allow shortages?  Explain the basis for your answer.