$5.$A semi$-$automatic production machine must be tended by a worker $100\%$ of the time to

load and unload parts. Cost of the starting parts $=$$$\frac{0\mathrm{.}25}{p}c.$ The job runs several months so

setup can be neglected. The equipment cost rate of the machine $=$$$\frac{24\mathrm{.}00}{h}r$ including

applicable overhead costs. The worker's cost rate $=$$$\frac{21}{h}r$ including applicable labor

overhead rate. Each cycle, the actual process time $=36sec,$ and time to load and unload

the part $=14sec.$ A proposal has been made to install an automatic parts$-$loading$-$and$-$

unloading

device on the machine, which would cost $$48,000$ and would reduce the parts loading$-$

and$-$unloading time to $5$ sec each cycle. Its expected life $=4yr.$ The device would

also relieve the worker from full$-$time attention to the machine. Instead, the worker could

tend four machines, effectively reducing the labor cost to $25\%$ of its current rate for each

machine. The operation runs $250$ days per year, $8$ hours per day. Assume availability $=$

$100\%$ and scrap rate $=0.$ Determine the cost per part $($a$)$ without the parts loading device and

$($b$)$ with the parts loading device installed. $($c$)$ How many days of production are

required to pay for the automatic loading device? In other words, find the breakeven point.