Question

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 155 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 175 components per hour. At present, components are produced eight hours a day and five days a week. Management believes that if need arises, it can add a second shift of eight hours for the assembly lines.

a. Determine the process capacity (number of components produced per week) of the entire process. Process capacity 6,000 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)? New process capacity 8,000 units per week b-2. Which of the three operations limits the capacity? Drilling machines O Final assembly line O Assembly line 1 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? New capacity 10,000 units per week

     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 cent per part. The total overhead cost has been calculated as $1,600 per week. The depreciation cost for equipment has been calculated as $30 per week.

--Determine the cost per unit output for part b. (Round your answer to 2 decimal places.)

cost per unit

--Determine the cost per unit output for part c. (Round your answer to 2 decimal places.)

cost per unit

--

The product is sold at $4 per unit. Assume that the cost of a drilling machine (fixed cost) is $28,000 and the company produces 8,200 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? (In your calculations, use the two-digit cost per unit from page d-1. Round your answer to the nearest whole number.)

-

-

Answer 1

a.

Capacity of assembly line 1 = 155 units/hour × 8 hours/day × 5 days/week

= 6,200 units/week.

Capacity of drill machines = 3 drill machines × 50 parts/hour × 8 hours/day × 5 days/week

= 6,000 units/week.

Capacity of final assembly line = 175 units/hour × 8 hours/day × 5 days/week

= 7,000 units/week.

The capacity of the entire process is 6,000 units per week, with drill machine limiting the overall capacity.

b-1.

Capacity of assembly line 1 = 155 units/hour × 16 hours/day × 5 days/week

= 12,400 units/week.

Capacity of drill machines = 4 drilling machines × 50 parts/hour × 8 hours/day × 5 days/week

= 8,000 units/week.

Capacity of final assembly line = 175 units/hour × 16 hours/day × 5 days/week

= 14,000 units/week.

The capacity of the entire process is 8,000 units per week,

(b-2) with drilling machines limiting the overall capacity.

c-1.

Capacity of assembly line 1 = 155 units/hour × 16 hours/day × 5 days/week

= 12,400 units/week.

Capacity of drill machines = 5 drilling machines × 50 parts/hour × 8 hours/day × 5 days/week

= 10,000 units/week.

Capacity of final assembly line = 175 units/hour × 12 hours/day × 5 days/week

= 10,500 units/week.

The capacity of the entire process is 10,000 units per week, with drill machine limiting the overall capacity.

Cost per unit when output for part b

Cost per unit when output = 8,000 units.

Item Calculation Cost

Cost of part A = $0.40 × 8,000 = $3,200

Cost of part B = $0.35 × 8,000 = 2,800

Cost of part C = $0.15 × 8,000 = 1,200

Electricity = $0.02 × 8,000 = 160

Assembly 1 labor = $0.25 × 8,000 = 2,000

Final assembly labor = $0.25 × 8,000 = 2,000

Drilling labor = $0.10 × 8,000 = 800

Overhead $ 1,600 per week = 1,600

Depreciation $ 30 per week = 30

Total $ 13,790

Cost per unit = Total cost per week/Number of units produced per week

= $13,790/8,000

= $1.72

Cost per unit when output for part c

Cost per unit when output = 10,000 units.

Item Calculation Cost

Cost of part A = $0.40 × 10,000 = $4,000

Cost of part B = $0.35 × 10,000 = 3,500

Cost of part C = $0.15 × 10,000 = 1,500

Electricity = $0.02 × 10,000 = 200

Assembly 1 labor = $0.25 × 10,000 = 2,500

Final assembly labor = $0.25 × 10,000 = 2,500

Drilling labor = $0.10 × 10,000 = 1,000

Overhead $ 1,600 per week = 1,600

Depreciation $ 30 per week = 30

Total $ 16,830

Cost per unit = Total cost per week/Number of units produced per week

= $16,830/10,000

= $1.68

BREAKEVEN CALCULATION

Cost per unit when output = 8,200 units.

Item Calculation Cost

Cost of part A = $0.40 × 8,200 = $3,280

Cost of part B = $0.35 × 8,200 = 2,870

Cost of part C = $0.15 × 8,200 = 1,230

Electricity = $0.02 × 8,200 = 164

Assembly 1 labor = $0.25 × 8,200 = 2,050

Final assembly labor = $0.25 × 8,200 = 2,050

Drilling labor = $0.10 × 8,200 = 820

Overhead $ 1,600 per week = 1,600

Depreciation $ 30 per week = 30

Total $ 14,094

Cost per unit = Total cost per week/Number of units produced per week

= $14,094/8,200

= $1.72

Let X = the number of units that each option will produce.

When the company buys the units, the cost is $3.00 per unit (3X). When it manufactures the units, they incur a fixed cost of $112,000 (4 drilling machines at $28,000 a piece) and a per unit cost of $1.72. Therefore, 112,000 + 1.72X is the cost of this option. Set them equal to each other and solve for X to determine the breakeven point.

3X = 112,000 + 1.72X

X = 87,500 units.

Therefore, it is better to buy the units when you produce less than 87,500, and better to produce them when demand is greater than 87,500 units.