A company is about to begin production of a new product The manager of a department that is asked to produce one of the components wants to know if there is enough machine time avallable. The machine will produce the item at a rate of $250$ units a day Ninety$-$five units will be used dally in assembling the final product. The company operates five days a week, $50$ weeks a year. The manager estimates that it will take almost a full day to get the machine ready for a production run, at a cost of $$240.$ Inventory holding cost will be $$10$ per unit per year.

$0.$ What production run quantity should be used to minimize total annual setup and holding cost? $($Do not round intermedlate calculations. Round the Mnal answer to the nearest whole number.$)$

Production run quantity Junits

b$.$ What is the length of a production run $($In days$)?($Do not round intermediate calculations. Round the final enswer to $2$ decimal places.$)$

Run length days

c$.$ During production, at what rate will inventory bulld up$?$

Rate units

c$.$ If the manager needs to run another job between runs of this job, and needs a minimum of $9$ days per cycle of this job for the other Job, will there be enough time?

Yes

No