Product cycle time is the time it takes for raw materials to be transformed into a fi nished

product. A fi rm makes $1000$ products per day. Before it is sold, each product represents

$$200$ in materials and labor.

$($a$)$ If the cycle time is $12$ days, how many dollars are tied up with in$-$process inventory? If the company$$s internal interest rate is $10$ percent, what is the annual cost

due to in$-$process inventory?

$($b$)$ If the cycle time is reduced to $8$ days as a result of process improvement, what is

the annual cost saving?