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 assembing 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:

a$.$ What production run quantity should be used to minimize total annual setup and holding cost? $($po not round intermediate celculations. Round the final snswer to the neerest whole number:$)$

Production run quantity units

b$.$ What is the length of a production run $($in days$)?($Do not round hrermedlate calculetions. Found the final enswer to $2$ decimal plecesing

Run length days

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

Rate units

d$.$ If the manager needs to run anotherjob 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