Rick Jerz is attempting to perform an inventory analysis on one of his most popular products. Annual demand for this

product is $6,000$ units; carrying cost is $$30$ per unit per year; order costs for his company typically run nearly $$50$

per order; and lead time averages $5$ days. $($Assume $250$ working days per year.$)$

a$)$ The economic order quantity is $141\mathrm{.}42$ units $($round your response to the nearest whole number$).$

b$)$ The average inventory is $71$ units $($round your response to the nearest whole number$).$

c$)$ The optimal number of orders per year is $42\mathrm{.}55$ orders $($round your response to the nearest whole number$).$

d$)$ The optimal number of working days between orders is $5\mathrm{.}81$ days $($round your response to two decimal places$).$

e$)$ The total annual inventory cost $($carrying cost $+$ ordering cost$)$ is $$,($round your response to the nearest cent$).$