Problem # $7$ Inventory Analysis

Ceramics Direct produces tiles for luxury flooring. The demand per month is $700$ pounds of tile. Ceramics Direct can produce $1500$ pounds of tile per month. Since the machinery gets dirty and must be cleaned before every batch the setup cost if $$300.$ It cost $$10$ to produce one pound of tile. The inventory cost is $30\%$ of annual cost. There can be a chance of backlogging. The two types are loss of goodwill, which is about $$20$ per pound. Shortage penalty is $$1\mathrm{.}50$ per pound short every month. Find the economic order quantity, optimal backorder, and annual total cost of inventory.