# math questions be done one hour

Please show solution steps.

1. A furniture store expects to sell 640 sofas at a steady rate next year. The manager of the store plans to order these sofas from the manufacturer by placing several orders of the same size spaced equally throughout the year. The ordering cost for each delivery is \$160 and the carrying costs, based on the average number of sofas in inventory, amount to \$32 per year for one sofa. Determine the economic order quantity that minimizes the inventory cost, and then and the minimum inventory cost.

2. A sporting equipment distributor expects to sell 10,000 cases of tennis balls during the coming year at a steady rate. Yearly carrying cost (to be determined on the average number of cases in stock during the year) are \$10 per case, and the cost of placing an order with the manufacturer is \$80. Determine the economic order quantity, that is, the order quantity that minimizes the inventory cost.

3. A certain company makes a laboratory microscopes. Setting up each production run costs \$2,500. Insurance costs, based on the average number of microscopes in the warehouse, mount to \$20 per microscope per year. Storage costs, based on the maximum number of microscopes in the warehouse, amount to \$15 per microscope per year. If the company expects to sell 1,600 microscopes at a fairly uniform rate throughout the year, determine the number of production runs that will minimize the company’s overall expenses.