### What is the lowest total cost

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7) Weedandfeed Corporation retails chemicals for homes.  One of Weedandfeed's best selling pesticides is Pest-be-gone.  The product is ordered from a wholesaler at a price of \$600 per 100 pounds.  100,000 pounds of Pest-be-gone are estimated to be needed next year.  Weedandfeed will use one of the following purchasing options for acquiring its product.

• It can order in the 1-15,000 pound range.  If it selects this option, the holding cost is 35% of the acquisition cost per pound per year, and the ordering cost is \$1,500 per order.   If it selects this option, it can order any quantity as long as it is between 1 and 15,000 pounds
• As the second option, Weedandfeed can buy Pest-be-gone in quantities greater than 15,000 pounds.  If it selects this option, it can order any quantity as long as it at least 15,001 pounds.  If it selects this option, then the holding cost drops to 25% of the acquisition cost per pound per year because the supplier gives special late-payment privileges that reduce the interest charges that must ordinarily be paid to finance the inventory.  However, ordering costs increase to \$2,500 per order because of the extra handling costs.

a)  Based on this information and wanting to use the low cost strategy, what is the optimal order quantity that Weedandfeed should select for acquiring its Pest-be-gone next year? What is the lowest total cost for each of the two purchase options?

b)  For the optimal order quantity selected in a) that provides the lowest total cost, determine the number of orders per year, time between orders, and the reorder point.  There are 350 working days per year and the lead time is 5 days.

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