Question

Ima Neworker requires 30 minutes to produce her first unit of output. If her learning curve rte is 65%, how many units will be produced before the output rate exceeds 12 units per hour?

Answer 1

Answer:

Approximately 18 units will be produced before the output rate exceeds 12 units per hour.

Step-by-step explanation:

The learning curve formula is given by:

$Y = aX^{b}$

In which:

Y is the average time per unit.

X is the cumulative number of units produced.

a is the time required to produe the first unit

b = log of learning rate/log 2

In our problem, we have:

Y = 12 units per hour. We are working in minutes, what is the average time per unit?

60 minutes - 12 units

Y minutes - 1 unit

$12Y = 60$

$Y = 5$

So Y = 5.

X is the value we want to find

a = 30

b = $\frac{log 0.65}{log 2}=-0.6215$

So

$Y = aX^{b}$

$5 = 30X^{-0.6215}$

$\frac{1}{6} = \frac{1}{X^{0.6215}}$

$X^{0.6215} = 6$

$\sqrt[0.6215]{X^{0.6215}} = \sqrt[0.6215]{6}$

$X = 17.86$

Approximately 18 units will be produced before the output rate exceeds 12 units per hour.