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 available. The machine will

produce the item at a rate of $200$ units a day. Eighty units will be used

daily in assembling the final product. The company operates five days aweek, $50$ weeks a year. The manager estimates that it will take almost a$$full day to get the machine ready for a production run, at a cost of $$300.$Inventory holding cost will be $$10$ per unit per year. LO$3$

a$.$ What production run quantity should be used to minimize total annual

setup and holding cost?

b$.$ What is the length of a production run $($in days$)?$

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

d$.$ If the manager needs to run another job between runs of this job, and

needs a minimum of $10$ days per cycle of this job for the other job,

will there be enough time?