Bailey Distributing Company sells small appliances to hardware stores in the southern California area. Michael Bailey, the president of the company, is thinking about changing the credit policies offered by the firm to attract customers away from competitors. The current policy calls for a $\frac{1}{10},$ net $30,$ and the new policy would call for a $\frac{3}{10},$ net $50.$ Currently $40$ percent of Bailey customers are taking the discount, and it is anticipated that this number would go up to $50$ percent with the new discount policy. It is further anticipated that annual sales would increase from a level of $$200,000$ to $$250,000$ as a result of the change in the cash discount policy.

The increased sales would also affect the inventory level carried by Bailey. The average inventory carried by Bailey is based on a determination of an EOQ. Assume unit sales of small appliances will increase from $20,000$ to $25,000$ units. The ordering cost for each order is $$100$ and the carrying cost per unit is $$1($these values will not change with the discount$).$ The average inventory is based on EOQ$/2.$ Each unit in inventory has an average cost of $$6\mathrm{.}50.$

Cost of goods sold is equal to $65$ percent of net sales, general and administrative expenses are equal to $10$ percent of net sales, and interest payments of $12$ percent will be necessary only for the increase in the accounts receivable and inventory balances. Taxes will equal $25$ percent of before$-$tax income.

b$.$ Determine EOQ before and after the change in the cash discount policy. Translate this into average inventory $($in units and dollars$)$ before and after the change in the cash discount policy.