Question

Question 4 1 pts A furniture maker has an order for 58 identical tables. If the furniture maker estimates his learning curve at 84% and can reach steady production of 7 hours per table on the 4th table, how long should it take to make all the tables? Express your answer in hours to the nearest whole hour.

Answer 1

The standard equation for calculating using a learning curve is T_n=T₁n^b.

In this case, given the information for the 4th unit,

T_n= 7hours (amount of time taken for the 4th unit)

n= the unit in consideration (the 4th unit in this case)

T₁= the amount of time taken for the first unit

b= ln(p)/ln(2); where p= learning percentage (84% or 0.84 here).

the value of b= -0.25

Calculating the time taken for the first unit (T₁),

7= T₁ * 4^-0.25

T₁= 9.89, which is approximately 10 hours for the first unit.

Now, finding the total time taken for all 58 tables is essentially finding the sum of a geometric progression;

; where Sn is the sum of all 58 tables, a₁=T₁= 10 hours, r is the common ratio which is 0.84

S_n= 10(1- 0.84⁵⁸) / (1-0.84)

S_n= 62.5, which is approximately 63 hours for all 58 tables.