2. Award:o out of 416 points Show my a Show my answer Problem 6-5 Jack Simpson,
ID: 421317 • Letter: 2
Question
2. Award:o out of 416 points Show my a Show my answer Problem 6-5 Jack Simpson, contract negotiator for Nebula Airframe Company, is currently involved in bidding on a follow-up government contract. In gathering cost data from the first three units, which Nebula produced under a research and development contract, he found that the first unit took 2,500 labor hours, the second took 1,750 labor hours, and the third took 1,650 hours. Use Exhibit 6.5 In a contract for three more units, how many labor hours should Simpson plan for? (Round your answer to the nearest whole number.) Number of labor 3,313 t 1 hours Explanation: You can figure this out by using the cumulative factors in Exhibit 6.5. You want to find the time needed for the 4th through 6th units. That is equal to the time for all 6 units minus the time for the first 3. So take the cumulative factor for 6 units, subtract off the cumulative factor for 3 units, and multiply the result by the first unit's production time. Use the ratio of times for the 1St and 2nd units to estimate the relevant learning percentage.Explanation / Answer
The following question is solved using the concept of learning curve which is based on the idea that the time taken to complete a task is shorter than the time that was taken to complete the same task in the past. This means that the manufacturer gained experience and used it to improve themselves.
We will use the following formula to find out the cumulative times to complete a specific number of units.
Y = aXb
where,
Y = the cumulative average time per unit.
X = the total number of units produced.
a = time needed to produce the first unit.
b = log of the learning rate/log of 2.
Time taken to produce the first unit = 2500 hours
Time taken to produce the second unit = 1750 hours
The learning curve is found by the ratio of time taken to complete the second unit to the time taken to complete the first unit
= 1750 / 2500 = 0.7 or 70% learning rate
Now we will use the above formula to find out the cumulative time taken to complete 6 units.
Here, X = 6, a = 2500 b = log (0.7)/ log2
b = -0.514
Y = 2500 * 6-0.514
Y = 995.33 hours
Total time to complete 6 units, = X times Y
= 6 * 995.33
= 5972.02 hours
Now we will use the above formula to find out the cumulative time taken to complete 3 units
Here, X = 3, a = 2500 b = log (0.7)/ log2
b = -0.514
Y = 2500 * 3-0.514
Y = 1421.34 hours
Total time to complete 3 units, = X times Y
= 3 * 1421.34
= 4264.03 hours
The total time taken to complete units 4, 5, and 6 is the difference in cumulative time taken to complete the first 6 units to the time taken to complete the first 3 units.
= 5972.02 - 4264.03
= 1709 hours approximately.
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