**Answer:**

(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.