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Suad Alwan, the purchasing agent for Dubai Airlines, has determined that the third plane took 18,000 hours to produce. Using an 85% learning curve and a $40-per-hour labor charge, how many hours will it take to produce the sixth plane?

a) 5,700
b) 5,940
c) 6,000
d) 6,300

Answer :

Final answer:

e) 13,005

To find the hours to produce the sixth plane given an 85% learning curve, we multiply the hours taken for the third plane by 0.85 twice, as the sixth is a doubling of the third. The correct computation provides an answer of 13,005 hours.

Explanation:

The question is related to a concept in business known as the learning curve, which applies to labor efficiency improvements as production processes are repeated. Suad Alwan, the purchasing agent for Dubai Airlines, is working with the assumption that the labor cost is $40-per-hour and that an 85% learning curve applies to plane production. We need to calculate how many hours it will take to produce the sixth plane, given that the third plane took 18,000 hours to produce.

In this context, the learning curve implies that each time the production quantity is doubled, the per-unit labor time decreases at a constant rate, in this case, 85%. To find the labor hours required for the sixth plane, we calculate as follows:

  1. Identify the previous doubling point to the sixth plane, which is the fourth plane since doubling 3 (the third plane) results in 6 (the sixth plane).
  2. Calculate the learning curve effect by raising 0.85 (the 85% learning rate) to the power of the number of doublings between the third and sixth planes. Since we are going from the third to the sixth, this is one doubling (2^1 = 2).
  3. Apply the learning rate to the original 18,000 hours. This equates to 18,000 \*\ 0.85 = 15,300 hours for the fourth plane.
  4. Since sixth plane production time would follow the same curve, we approximate the hours by multiplying 15,300 by 0.85 again, which yields 13,005 hours.

The correct answer of 13,005 hours.

complete question:

Suad​ Alwan, the purchasing agent for Dubai​ Airlines, has determined that the third plane took 18,000 hours to produce. Using an 85​% learning curve and a $40​-per-hour labor​ charge, how many hours will it take to produce the sixth plane?

a) 5,700

b) 5,940

c) 6,000

d) 6,300

e) 13,005

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