Question $2.$ A company is about to begin production of a new product. The manager of the department that produces one of the components for the product wants to know how often the machine needed to produce the item will be available for other work.

The machine produces the item at a rate of $150$ units a day. Seventy units are used daily in assembling the final product. Assembly takes place 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 each production run, at a cost of $$300.$ Inventory holding costs will be $$10$ per unit. Round to two decimal points $(50$ points, $10$ points each$)$

$\backslash$table$[[$a$.$ What run quantity $($optimal run size$)$ will$],[$minimize total annual costs $($EPQ$)?],[$b$.$ What is the length of a production run$],[($run time$)$ in days?$],[$c$.$ During production, how many units a$],[$day go to inventory as opposed to into$],[$production$?],[$d$.$ What is the cycle time for optimal run$],[$time$?],[\backslash$table$[[$e$.$ How many days will be available$],[$between the production runs of this new$],[$item$,$ allowing for the production of other$],[$products during the downtime?$]]]]$