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 $170$ 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 $70$ 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 $190$ 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 $25$ cents per part for each assembly line; the cost of drilling labor is $10$ cents per part. For drilling, the cost of electricity is $2$ cents per part. The total overhead cost has been calculated as $$1,400$ per week. The depreciation cost for equipment has been calculated as $$30$ per week.

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

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$)?$

b$-2.$ Which of the three operations limits the capacity?

Drilling machines

Assembly line

Final assembly line

c$-1.$ Management decides to run a second shift of eight 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?

c$-2.$ Which of the three operations limits the capacity?

Final assembly line

Drilling machines

Assembly line

d$-1.$ Determine the cost per unit output for part b$.$

Note: Round your answer to $2$ decimal places.

d$-2.$ Determine the cost per unit output for part c$.$

Note: Round your answer to $2$ decimal places.

e$.$ The product is sold at $$5\mathrm{.}00$ per unit. Assume that the cost of a drilling machine $($fixed cost$)$ is $$36,000$ and the company produces $7,000$ units per week. Assume that four drilling machines are used for production. If the company had an option to buy the same part at $$4\mathrm{.}00$ per unit, what would be the break$-$even number of units?

Note: In your calculations, use the two$-$digit cost per unit from part d$-1.$ Round your answer to the nearest whole number.