Question

Johnson Industries received a contract to develop and produce four high-intensity long-distance receiver/transmitters for cellular telephones. The first took 2,600 labor hours and $44,000 worth of purchased and manufactured parts; the second took 2,240 labor hours and $42,240 in parts; the third took 2,060 labor hours and $40,980 in parts; and the fourth took 1,882 labor hours and $39,710 in parts.

     Johnson was asked to bid on a follow-on contract for another dozen receiver/transmitter units. (Hint: There are two learning curves—one for labor and one for parts.)

    
a. How many labor hours should Johnson estimate are needed for the additional 12 units? (Round your answer to the nearest whole number.)

b. How much should Johnson estimate the parts cost will be for the additional 12 units? (Round your answer to the nearest dollar amount.)

Answer 1

(a)

Units	Labor hrs.	Rate of decrease
1	2,600
2	2,240	2240 / 2600 = 0.86
4	1,882	1882 / 2240 =0.84
	Avg.	0.85

So, the learning rate is 85%.

The cumulative improvement factor for 16 units = 10.38
The cumulative improvement factor for 4 units = 3.345

So, the labor hours required to produce an additional 12 units = Labor-hrs. for the first unit * (10.38 - 3.345) = 2600* (10.38 - 3.345) = 18,291 hrs.

(b)

Units	Cost	Rate of decrease
1	44,000
2	42,240	0.96
4	39,710	0.94
	Avg.	0.95

So, the learning rate is 95%

The cumulative improvement factor for 16 units = 13.91 (from table)
The cumulative improvement factor value for 4 units = 3.774

So, the cost to produce an additional 12 units = Cost of the first unit * (13.91 - 3.774) = 44000* (13.91 - 3.774) = $445,984