It took 60 hours to make the first unit of a product. After the second and third units were made, the learning curve was estimated to be 80%. At $10 per hour, estimate the labour bill for the fourth unit. (Use at least three decimals in the exponent if you use the logarithmic approach.)
A) $400 or less
B) from $400 to $420
C) from $420 to $440
D) from $1800 to $2000
E) over $2000

Question

Quizplus · Accepted Answer

The learning curve formula is Tn = T1 * n^b, where Tn is the time it takes to produce the nth unit, T1 is the time it takes to produce the first unit, n is the unit number, and b is the learning rate exponent. The learning rate exponent can be calculated using the formula b = log(learning percentage) / log(2). In this case, b = log(0.80) / log(2) = -0.3219. Therefore, the time to produce the fourth unit is T4 = 60 * 4^-0.3219 = 60 * 0.759 = 45.54 hours. At $10 per hour, the labor bill for the fourth unit is $455.40, which is in the range of $400 or less.

It Took 60 Hours to Make the First Unit of a Product