Problem $7-15($Static$)$

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 $40,35,$ and $15$ cents per piece, respectively. Parts A and $B$ are assembled first on assembly line $1,$ which produces $140$ 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 $50$ 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 $160$ components per hour. At present, components are produced eight hours a day and 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 $15$ cents per part. For drilling, the cost of electricity is one 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

units per weeK

B$)$ suppose a second shift of $8$ hours is run for assmebly 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 $8$ hours a day. What is the new process capacity?

c$)$ management decides to run a second shift of $8$ hours for assembly line $1,$ plus a second shift of only four hours for the final assembly line. Five of the six drilling machines operate for eight hours a day. What is the new capacity?

D$)$ determine the cost per unit output for part b

E$)$ determine the cost per unit output for part c

F$)$ the product is sold at $$4$ per unit. Assume that the cost of a drilling machine fixed is $$30000$ and the company produces $8000$ units per week. Assume that four drilling machines are used for production. If the company had an option to buy the same part at $$3$ per unit, what would be the break even number of units?