A manager must decide which type of machine to buy, A, B, or C. Machine costs (p
ID: 448903 • Letter: A
Question
A manager must decide which type of machine to buy, A, B, or C. Machine costs (per individual machine) are as follows:
Machine Cost
A $40,000
B $30,000
C $80,000
Product forecasts and processing times on the machines are as follows:
PROCCESSING TIME PER UNIT (minutes)
Product Annual Demand A B C
1 18,000 4 2 1
2 20,000 1 5 3
3 20,000 5 6 6
4 16,000 4 6 3
a. Assume that only purchasing costs are being considered. Compute the total processing time required for each machine type to meet demand, how many of each machine type would be needed, and the resulting total purchasing cost for each machine type. The machines will operate 10 hours a day, 230 days a year. (Enter total processing times as whole numbers. Round up machine quantities to the next higher whole number. Compute total purchasing costs using these rounded machine quantities. Enter the resulting total purchasing cost as a whole number. Omit the "$" sign.)
Total processing time in minutes per machine:
A _______________
B _______________
C _______________
Number of each machine needed and total purchasing cost
A $______
B $______
C $______
b. Consider this additional information: The machines differ in terms of hourly operating costs: The A machines have an hourly operating cost of $13 each, B machines have an hourly operating cost of $11 each, and C machines have an hourly operating cost of $12 each. What would be the total cost associated with each machine option, including both the initial purchasing cost and the annual operating cost incurred to satisfy demand? (Use rounded machine quantities from Part a. Do not round any other intermediate calculations. Round your final answers to the nearest whole number. Omit the "$" sign.)
Total cost for each machine
A _________
B__________
C__________
Explanation / Answer
a.
Calculate the total processing time required by different machines as shown below:
For Machine A = (Annual demand for product 1 × Processing time) + (Annual demand for product 2 × Processing time) + (Annual demand for product 3 × Processing time) + (Annual demand for product 4 × Processing time)
Therefore,
Processing minutes per year for machine A = (18000×4) + (20000×1) + (20000×5) + (16000×4)
= 2, 56,000 min
In the same way calculate the processing time for rest of the machine as shown below:
For machine B = (18000×2) + (20000×5) + (20000×6) + (16000×6)
= 3, 52,000 min
For machine C = (18000×1) + (20000×3) + (20000×6) + (16000×3)
= 2, 46,000 min
Calculate the Number of machine needed by using the formula as shown below:
Total number of machine needed per year = total processing time required by a machine / Total processing time available in a year
Therefore, number of machine:
A = 2, 56,000 / (10 *230*60) = 1.85 or 2 machines
B = 208,000 / (10*230*60) = 2.55 or 3 machines
C = 122,000 / (10*230*60) = 1.78 or 2 machines
Calculate the total cost by using the formula as shown below:
Purchase cost = (Machine cost ×Number of machine)
Therefore,
Therefore, number of machine:
A = 2, 56,000 / (10 *230*60)
= 1.85 or 2 machines
B = 208,000 / (10*230*60)
= 2.55 or 3 machines
C = 122,000 / (10*230*60)
= 1.78 or 2 machines
Calculate the total cost by using the formula as shown below:
Purchase cost = (Machine cost ×Number of machine)
Therefore,
Total purchase cost for:
A = (40000 × 2)
= $ 80,000
B = (30,000 × 3)
=$90,000
C = (80000×2)
= 1, 60,000
b.
Calculate the total operating cost as shown below:
Total operating cost = Total Purchase cost + Operating cost
Therefore,
Total operating Cost A = (80,000) + ((256,000 / 60)*13)
= 80,000 + 55,467
= $1, 35,467
Total operating Cost B = (9,000) + ((3, 52,000 / 60)*11)
= 90,000 + 64,533
= $1, 54,533
Total operating Cost C = (1, 60,000) + ((246,000 / 60)*12)
= 1,60,000 + 49,200
= $2,09,200
Therefore machine 1 should be purchased as it has the lowest operating cost.
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