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 labor 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 labor time for the fourth unit can be calculated using the learning curve formula: Tn = T1 * n^(log b / log 2), where Tn is the time required for the nth unit, T1 is the time required for the first unit, n is the unit number, and b is the learning rate (in this case, 80% or 0.8). For the fourth unit, the formula becomes T4 = 60 * 4^(log 0.8 / log 2). Calculating the exponent: log 0.8 / log 2 ≈ -0.322 (using at least three decimals as instructed). Thus, T4 ≈ 60 * 4^(-0.322) ≈ 60 * 0.6 ≈ 36 hours. At $10 per hour, the labor bill for the fourth unit is 36 * $10 = $360, which is $400 or less.

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