Problem $7-15($Algo$)$

The Goodparts Company produces a component that is subsequently used in the aerospace industry. The component consists of three parts $($A$,$ B$,$ and C$)$ that are purchased from outside and cost $35,30,$ and $10$ cents per piece, respectively. Parts A and $B$ are assembled first on assembly line $1,$ which produces $185$ components per hour. Part $C$ undergoes a drilling operation before being finally assembled with the output from assembly line $1.$ There are, in total, six drilling machines, but at present only three of them are operational. Each drilling machine drills part $C$ at a rate of $80$ parts per hour. In the final assembly, the output from assembly line $1$ is assembled with the drilled part $C.$ The final assembly line produces at a rate of $205$ components per hour. At present, components are produced eight hours a dayzand five days a week. Management believes that if the need arises, it can add a second shift of eight hours for the assembly lines.

The cost of assembly labor is $30$ cents per part for each assembly line; the cost of drilling labor is $10$ cents per part. For drilling, the cost of electricity is $1$ cent per part. The total overhead cost has been calculated as $$1,200$ per week. The depreciation cost for equipment has been calculated as $$30$ per week.

a$.$ Determine the process capacity $($number of components produced per week$)$ of the entire process.

Process capacity

$1$ units per week

b$-1.$ Suppose a second shift of eight hours is run for assembly line $1$ and the same is done for the final assembly line. In addition, four of the six drilling machines are made operational. The drilling machines, however, operate for just eight hours a day. What is the new process capacity $($number of components produced per week$)?$

$2\mathrm{.}25$ units per week