Answer to question a :
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