A machine tool produces $26$ components for an assembled product.

These are the only parts produced by the machine. To keep in$-$process

inventories low, a batch size of $75$ units is produced for each

component. Demand for the product is $900$ units$/$yr$.$ Production

downtime costs $$120/$hr$.$ Changeover time between batches is $1\mathrm{.}5$ hr$,$

and average cycle time per part $=4\mathrm{.}0$ min. The annual holding cost for

each of the $26$ parts is $$1\mathrm{.}60/$pc$.($a$)$ Determine total annual inventory

cost for the $26$ parts. $($b$)$ Is the given production schedule feasible for a

one$-$ shift operation? That is$,$ can $900$ units of each of the $26$

components be completed in $2000$ hours? If so$,$ how many idle hours of

machine time occur in the $2000$ hours? If not, how many overtime

hours must be authorized during the year?

$2$