A local company produces an erasable programmable read$-$only memory $($EPROM$)$ for several industrial clients. It has experienced a relatively flat demand of $2,500$ units per year for the product. The EPROM is produced at a rate of $10,000$ units per year. The accounting department has estimated that it costs $$50$ to initiate a production run, each unit costs the company $$2$ to manufacture, and the cost of holding is based on a $30$ percent annual interest rate. Determine the optimal size of a production run, the length of each production run, and the average annual cost of holding and setup. What is the maximum level of the on$-$hand inventory of the EPROMs?