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

Answer to question B :

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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