ExpertMedium2 marksShort Answer
ACCA · Question 10 · Budgeting and Control
Section A
Oceanic Luxury Yachts is assembling a new class of custom yachts. The assembly process is subject to a learning curve.
The time taken to assemble the first yacht was 1,000 hours. The learning rate is 81%, which corresponds to a learning index (b) of -0.304.
Using the formula Y = ax^b, what is the cumulative average time per yacht (in hours) to assemble the first 4 yachts? (Round to the nearest whole hour)
Section A
Oceanic Luxury Yachts is assembling a new class of custom yachts. The assembly process is subject to a learning curve.
The time taken to assemble the first yacht was 1,000 hours. The learning rate is 81%, which corresponds to a learning index (b) of -0.304.
Using the formula Y = ax^b, what is the cumulative average time per yacht (in hours) to assemble the first 4 yachts? (Round to the nearest whole hour)
How to approach this question
Apply the formula Y = ax^b. a = 1000, x = 4, b = -0.304. Calculate 1000 * (4^-0.304).
Full Answer
Using the doubling rule:
Average time for 1 unit = 1,000 hours.
Average time for 2 units = 1,000 * 0.81 = 810 hours.
Average time for 4 units = 810 * 0.81 = 656.1 hours.
Rounding to the nearest whole hour gives 656.
Alternatively, using the formula: Y = 1000 * 4^(-0.304) = 1000 * 0.6561 = 656.1.
Common mistakes
Calculating the total time for 4 units instead of the cumulative average time, or applying the 81% to the total time.
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