# Problem 5-11 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 \$ 70,000 B \$ 60,000 C \$ 50,000 Product forecasts and processing times on the machines are as follows: PROCCESSING TIME PER UNIT (minutes) Product Annual Demand A B C 1 28,000 1 2 2 2 21,000 6 5 4 3 21,000 1 6 2 4 7,000 5 1 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 8 hours a day, 250 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 \$14 each, and C machines have an hourly operating cost of \$15 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

Total processing time in any machine = Sum of ( Processing time / unit x Annual demand ) for all 4 products

Total processing time required for machine A

= 28000 x 1 + 21000 x 6 + 21000 x 1 + 7000 x 5

= 28000 + 126000 + 21000 + 35000

= 210000 MINUTES

Total processing time required for machine B

= 28000 x 2 + 21000 x 5 + 21000 x 6 + 7000 x 1

= 56000 + 105000 + 126000 + 7000

= 294000 MINUTES

Total processing time required for machine C

= 28000 x 2 + 21000 x 4 + 21000 x 2 + 7000 x 3

= 56000+84000 + 42000 + 21000

= 203000 MINUTES

Total time for which a machine operates in a year

= 60 minutes/ hour x 8 hours/ day x 250 days

= 120000 minutes

Number of any machine required = Total processing time in any machine/ Total time for which a machine operates in a year – ROUNDED TO NEXT HIGHER WHOLE NUMBER

Thus number of machine A required = 248000/105600 = 210000/120000 = 1.75 ( 2 rounded to next higher whole number )

Total cost for machine A = \$70,000 / machine x 2 machines = \$140,000

Number of machine B required = 294000 / 120000 = 2.45 ( 3 rounded to next higher whole number )

Total cost for machine B = \$60,000 / machine x 3 machines = \$180,000

Number of machine C required = 203000/120000 = 1,69 ( 2 rounded to nearest whole number )

Total cost of machine C = \$50,000/ machine x 2 = \$100,000

Machine type

Number needed

Total cost ( \$)

A

2

140,000

B

3

180,000

C

2

100,000

Operating cost for any machine type = Hourly operating cost / 60 x Total time for which machines operate in a year

Operating cost for Machine A = \$13/60 x 210,000 = \$ 45500 ( rounded to nearest whole number)

Operating cost for Machine B = \$14/60 x 294,000 = \$ 68600 ( rounded to nearest whole number )

Operating cost for Machine C = \$15/60 X 203,000 = \$ 50750 ( rounded to nearest whole number )

Total cost associated with each machine option

= Total purchasing cost + Total operating cost

Therefore

Total cost for machine A = \$140,000 + \$45,500 = \$185,500

Total cost for machine B = \$180,000 +\$68600 = \$248,600

Total cost for machine C = \$100,000 +\$50750 = \$150,750

Machine type

Total cost ( \$)

A

185500

B

248600

C

150750

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