Answer:
Estimated time required to assemble the 20th unit= 8.836 hours
Explanation:
The learning curve theory states that as the cumulative output doubles the cumulative average time taken till date is reduced to a certain percentage of the previous time. This percentage is called learning rate; and is given as 85% in this question.
The cumulative average time is determined using the formula below:
Y= aX^b
a - time taken for the first unit produced
b = log LR/Log 2
X- cumulative units till date
Y - cumulative average time taken for X units
LR- Learning rate
<em>So we can apply this formula to our question</em>
b = Log 0.85%/Log 2 = -0.23446
15.882 = a * 5^(-0.23446)
15.882 = a * 0.685671
a =15.882/0.685671
a =23.16271007
Time taken for the first unit =23.16 hours
Estimated time taken to assemble 20th units:
= Total time for 20units -Total time for 19units
= (23.16×(20^-0.23446)×20) - (23.16×(19^-0.23446)×19)
= 229.4949 -229.4949
= 8.836 hours
Note: total time = Cumulative average time × Cumulative number of units
Estimated time required to assemble the 20th unit= 8.836 hours
