Problem 6-7 Johnson Industries received a contract to develop and produce four h

Question

Problem 6-7

Johnson Industries received a contract to develop and produce four high-intensity long-distance receiver/transmitters for cellular telephones. The first took 2,200 labor hours and $40,000 worth of purchased and manufactured parts; the second took 1,670 labor hours and $34,400 in parts; the third took 1,450 labor hours and $31,650 in parts; and the fourth took 1,236 labor hours and $28,900 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.) Use Exhibit 6.5.

    
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.)

Explanation / Answer

According to Learning curve theory, the time per unit decreases at a constant rate each time the output doubles (e.g., unit 1 to 2, 2 to 4, and 3 to 6). The ratios of these observed times will give us an approximate rate.

For Labor hours:

Unit 2/Unit 1 = 1670/2200 = 0.76

Unit 4/Unit 2 = 1236/1670 = 0.74

So, 75% learning curve for Labor hours

For Parts:

Unit 2/Unit 1 = 34400/40000 = 0.86

Unit 4/Unit 2 = 28900/34400 = 0.84

So, 85% learning curve for Parts

Total value for n units = Value for 1st unit*Total factor value

a)

1st unit = 2200

At 75% curve

Value for 16 units = 2200*7.635 = 16797 hours

Time for additional 12 units = Value for 16 units - Value for 1st 4 unit = 16797 - 2200 - 1670 - 1450 - 1236 = 10,241 hours

b)

1st unit = 40,000

At 85% curve

Value for 16 units = 40000*10.383 = 415,320 hours

Time for additional 12 units = Value for 16 units - Value for 1st 4 unit = 415320 - (40000 + 34400 + 31650 + 28900) = 280,370

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