High School

1. A production machine was purchased six years ago for an installed price of $530,000. At that time, it was anticipated that the machine would last 10 years and be used 4000 hours per year. However, it is now in need of major repairs that will cost $125,000. If these repairs are made, the machine will last four more years, operating 4000 hours per year. Applicable overhead rate = 30%. Assume availability = 100%.

Determine the equipment cost rate for this machine.

2. A stamping press produces sheet-metal stampings in batches. The press is operated by a worker whose labor rate = $15.00/hr and applicable labor overhead rate = 42%. Cost rate of the press = $22.50/hr and applicable equipment overhead rate = 20%. In one job of interest, batch size = 400 stampings, and the time to set up the die in the press takes 75 min. The die cost $40,000 and is expected to last for 200,000 stampings. Each cycle in the operation, the starting blanks of sheet metal are manually loaded into the press, which takes 42 sec. The actual press stroke takes only 8 sec. Unloading the stamping from the press takes 13 sec. Cost of the starting blanks = $0.23/pc. The press operates 250 days per year, 7.5 hours per day, but the operator is paid for 8 hours per day. Assume availability = 100% and scrap rate = 0%.

Determine:
(a) cycle time,
(b) average production rate with and without setup time included, and
(c) cost per stamping produced.

3. In a long-running high-production operation, the starting work material cost = $0.65/pc, and cycle time = 1.28 min. Equipment cost rate = $44.00/hr, and labor cost rate = $28.00/hr. Both rates include overhead costs. Tooling cost = $0.05/pc. Availability of the production machine = 95%, and the scrap rate = 4%.

Determine:
(a) production rate and
(b) finished part cost.

4. Using the data from problem #3, solve for the production rate and part cost if the machine availability = 100% and scrap rate = 0%.

Answer :

1. Equipment cost rate for the machine is $40.94 per hour.

2. (a) Cycle time is 4,563 seconds.

(b) Average production rate without setup time is 6.35 stampings/sec.

Average production rate with setup time is 0.88 stampings/sec.

(c) Cost per stamping produced is approximately $580.18.

3. (a) Production rate is approximately 0.78 parts/sec.

(b) Finished part cost is approximately $5.91 per part.

4. The production rate and part cost remain the same at 0.78 parts/sec and $5.91 per part.

1. Equipment cost rate for the machine:

To calculate the equipment cost rate, we need to consider the initial purchase cost, repairs, and the remaining years of useful life. The formula to calculate the equipment cost rate is:

Equipment Cost Rate = (Initial Cost + Repairs) / (Remaining Years * Annual Usage)

Initial Cost = $530,000

Repairs = $125,000

Remaining Years = 4

Annual Usage = 4,000 hours

Substituting the values into the formula:

Equipment Cost Rate = ($530,000 + $125,000) / (4 * 4,000) = $655,000 / 16,000 = $40.94/hour

Therefore, the equipment cost rate for the machine is $40.94 per hour.

2. (a) Cycle time:

The cycle time is the total time required to complete one batch of stampings, including setup time and operation time.

Cycle time = Setup time + Operation time + Unloading time

Setup time = 75 min = 75 * 60 sec = 4,500 sec

Operation time = Press stroke time + Loading time

Press stroke time = 8 sec

Loading time = 42 sec

Unloading time = 13 sec

Cycle time = 4,500 sec + (8 sec + 42 sec + 13 sec) = 4,500 sec + 63 sec = 4,563 sec

(b) Average production rate with and without setup time included:

Average production rate is the number of stampings produced per unit of time.

Without setup time:

Average production rate = Batch size / (Cycle time - Setup time)

Batch size = 400 stampings

Average production rate = 400 / (4,563 sec - 4,500 sec) = 400 / 63 sec ≈ 6.35 stampings/sec

With setup time:

Average production rate = Batch size / Cycle time

Average production rate = 400 / 4,563 sec ≈ 0.88 stampings/sec

(c) Cost per stamping produced:

Cost per stamping produced includes the labor cost, equipment cost, material cost, and overhead costs.

Cost per stamping produced = (Labor cost + Equipment cost + Material cost) / Batch size

Labor cost = Labor rate * Cycle time * (1 + Labor overhead rate)

Equipment cost = Equipment cost rate * Cycle time * (1 + Equipment overhead rate)

Material cost = Starting blanks cost

Labor rate = $15.00/hr

Labor overhead rate = 42%

Equipment cost rate = $22.50/hr

Equipment overhead rate = 20%

Starting blanks cost = $0.23/pc

Batch size = 400 stampings

Substituting the values into the formula:

Labor cost = $15.00/hr * 4,563 sec * (1 + 42%) = $15.00/hr * 4,563 sec * 1.42 = $97,446.30

Equipment cost = $22.50/hr * 4,563 sec * (1 + 20%) = $22.50/hr * 4,563 sec * 1.20 = $123,177.00

Material cost = $0.23/pc * 400 = $92.00

Cost per stamping produced = ($97,446.30 + $123,177.00 + $92.00) / 400 ≈ $580.18/stamping

3. (a) Production rate:

Production rate is the number of finished parts produced per unit of time.

Production rate = 60 / Cycle time

Cycle time = 1.28 min = 1.28 * 60 sec =76.8 sec

Production rate = 60 / 76.8 sec ≈ 0.78 parts/sec

(b) Finished part cost:

Finished part cost includes the labor cost, equipment cost, tooling cost, material cost, and overhead costs.

Finished part cost = (Labor cost + Equipment cost + Tooling cost + Material cost) / Production rate

Labor cost = Labor cost rate * Cycle time

Equipment cost = Equipment cost rate * Cycle time

Tooling cost = $0.05/pc

Labor cost rate = $28.00/hr

Equipment cost rate = $44.00/hr

Tooling cost = $0.05/pc

Material cost = $0.65/pc

Substituting the values into the formula:

Labor cost = $28.00/hr * 1.28 min = $28.00/hr * 1.28 * 60 sec = $2,073.60

Equipment cost = $44.00/hr * 1.28 min = $44.00/hr * 1.28 * 60 sec = $3,302.40

Tooling cost = $0.05/pc

Material cost = $0.65/pc

Finished part cost = ($2,073.60 + $3,302.40 + $0.05/pc + $0.65/pc) / 0.78 ≈ $5.91/part

4. If machine availability = 100% and scrap rate = 0%:

The production rate and finished part cost will remain the same as calculated in part 3 since machine availability and scrap rate do not affect these parameters. Therefore, the production rate will still be approximately 0.78 parts/sec, and the finished part cost will still be approximately $5.91/part.

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