It takes 3 minutes to load and 2 minutes to unload a machine. Inspection and packing times total 1 minute; travel between machines takes 2 minutes. Machines run automatically for 20 minutes. Operators cost $10 per hour; machines cost $30 per hour. Document all answers completely. a) What is the ideal machine assignment
b) If three machines are assigned to an operator, what is the duration of the repeating cycle? Will any machine of operator experience idle time, if so how long?
c) What is the cost per unit produced if three machines are assigned to an operator?

(a) The ideal machine assignment time is 7 minutes

(b) Duration of the repeating cycle is 25 minutes. Yes, there will be idle operator time of 7 minutes

(c) Cost per unit produced if three machines are assigned to an operator is $13.88 per unit

Explanation:

Loading = 3 minutes

Unloading = 2 minutes

Run time = 20 minutes

Inspection and packing times = 1 minute

Operators cost $10 per hour

Machines cost $30 per hour

(a) Ideal machine assignment = Machine cycle time ÷ Operator time per machine

Here, Machine cycle time = run time + load time + unload time

= 20 + 3 + 2

= 25  minutes

Operator time per machine = load time + unload time + inspection and packing time = 3 + 2 + 1 = 6

Hence, Ideal machine assignment = 25 ÷ 6 = 4.166=4.17 machine

(b) The number of machine assigned is less than ideal machine assignment hence, Operator will be idle.

Duration of repeating cycle = loading time + unloading time + machine run time = 3+2+20 = 25 minutes

Idle operator time = Cycle time - (number of machines assigned × (load time+ unload time+ inspection and packaging time))= 25- [3×(3+2+1)]

=25-18

=7 minutes

(c) Total cost of per unit produced = ((cost per operator hour + number of machines assigned × cost of per machine hour) × ((loading & unloading time + machine run time)÷60) )) ÷ number of machine

=( (10+[3×30]) × ((3+2+20) ÷ 60)) ÷ 3

=(100 × .416) ÷ 3

= 25 ÷ 3

= $13.88 per unit.

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