$1.$ The average part produced in a certain batch manufacturing plant must be processed sequentially through six machines on

average. Twenty $(20)$ new batches of parts are launched each week. Average operation time $=6$min., average setup time $=5$ hours,

average batch size $=25$ parts, and average nonoperation time per batch $=10$ hr$/$machine$.$ There are $18$ machines in the plant

working in parallel. Each of the machines can be set up for any type of job processed in the plant. The plant operates an average

of $70$ Production hours per week. Scrap rate is negligible. Determine $($a$)$ manufacturing lead time for an average part, $($b$)$ Plant

capacity, $($c$)$ plant utilization. $($d$)$ How would you expect the nonoperation time to be affected by the plant utilization?

$2.$ An Average of $20$ new orders are started through a certain factory each month. On average, an order consists of $50$ parts that are

processed sequentially through $10$ machines in the factory. The operation time per machine for each part $=15$ min. The

nonoperation time per order at each machine averages $8$ hours, and the required setup time per order $=4$ hours. There are a total of

$25$ machines in the factory working in parallel. Each of the machines can be set up for any type of job processed in the plant. Only

$*0\%$ of the machines are operational at any time$($the other $20\%$ are in repair or maintenance$).$ The plant operates $160$ hours per

month. However, the plant manager complains that a total of $100$ overtime machine$-$hours must be authorised each month in order

to keep up with the production schedule. $($a$)$ What is the manufacturing lead time for an average order? $($b$)$ What is the plant

capacity $($on a monthly basis$)$ and why must the overtime be authorized? $($c$)$ What is the utilization of the plant according to the

definition given in the text$/($d$)$ Determine the average level of work$-$in$-$process $($number of parts$-$in$-$process$)$ in the plant