$14\mathrm{.}7($A$)$ A plastic$-$injection molding plant will be built to produce $4,000,000$ molded parts$/$yr$.$ The plant will run three $8-$hr shifts per day, five days$/$wk$,52$ wk$/$yr$.$ For planning purposes, the average batch size $=5,000$ moldings, average changeover time between batches $=5$ hr$,$ and average molding cycle time per part $=22$ sec$.$ Assume Scrap rate $=2\%,$ and availability for each molding machine $=97\%,$ which applies to both run time and changeover time. $($a$)$ How many molding machines are required in the new plant? $($b$)$ What is the time required to produce each batch?