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	$	60,000
B	$	50,000
C	$	60,000

Product forecasts and processing times on the machines are as follows:

			PROCCESSING TIME PER UNIT (minutes)
Product	Annual Demand		A	B	C
1	15,000		2	4	2
2	25,000		6	2	3
3	15,000		3	5	5
4	20,000		3	4	2

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, 220 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 $14 each, B machines have an hourly operating cost of $12 each, and C machines have an hourly operating cost of $14 each. What would be the total cost associated with each machine option, including both the initial purchasing cost and the annual operating cost incurred to satisfy demand?(Use rounded machine quantities from Part a. Do not round any other intermediate calculations. Round your final answers to the nearest whole number. Omit the "$" sign.)

Total cost for each machine
A
B
C

Answer 1

a.

processing time required in machine A = 2*15000 + 6*25000 + 3*15000 + 3*20000 = 285000
processing time required in machine B = 4*15000 + 2*25000 + 5*15000 + 4*20000 = 265000
processing time required in machine C = 2*15000 + 3*25000 + 5*15000 + 2*20000 = 220000

Total available time = 220*8*60 minutes = 105600 minutes

No of Machine A required = 285000/105600 = 2.698863636 = 3 (Rounded to next whole number)

No of Machine B required = 265000/105600 = 2.509469697 = 3 (Rounded to next whole number)

No of Machine C required = 220000/105600 = 2.083333333 = 3 (Rounded to next whole number)

according to fixed cost,

Total fixed cost for machine A = 60,000*3 = 180,000

Total fixed cost for machine B =50,000*3 = 150,000

Total fixed cost for machine C = 60,000*3 = 180,000

So, based on annual fixed cost 2 machine B will cost least to satisfy the demand

b.

Hourly operating time required in machine A = 285000/60 = 4750

So operating cost = 4750*14 = 66500

Total cost = fixed cost + operating cost = 180000+66500 = 246500

Hourly operating time required in machine B = 265000/60 = 4416.666667

So operating cost = 4416.666667*12 = 53000

Total cost = fixed cost + operating cost = 150,000+53000 = 203000

Hourly operating time required in machine C = 220000/60 = 3666.666667

So operating cost = 3666.666667*14 = 51333.33334

Total cost = fixed cost + operating cost = 180000+51333.33334 = 231333.3333 = 231333 (Rounded to nearest whole number)