suppose a manufacturer of copiers has concluded that a 65 percent learning curve applies to the time a…

Explanation:

Step1: Recall learning - curve formula

The learning - curve formula is $T_x=T_1x^b$, where $T_x$ is the time required to produce the $x$th unit, $T_1$ is the time required to produce the first unit, $x$ is the cumulative number of units produced, and $b=\frac{\ln(\text{learning rate})}{\ln(2)}$.

Step2: Calculate $b$ for 65% learning rate

For a 65% learning rate, $b=\frac{\ln(0.65)}{\ln(2)}\approx - 0.621$. Given $T_1 = 5$ hours.

For $x = 2$:

$T_2=T_1\times2^b=5\times2^{- 0.621}=5\times0.65 = 3.3$ hours.

For $x = 3$:

$T_3=T_1\times3^b=5\times3^{-0.621}=5\times0.514\approx2.6$ hours.

Step3: Calculate $b$ for 55% learning rate

For a 55% learning rate, $b=\frac{\ln(0.55)}{\ln(2)}\approx - 0.857$.

For $x = 2$:

$T_2=T_1\times2^b=5\times2^{-0.857}=5\times0.55 = 2.8$ hours.

For $x = 3$:

$T_3=T_1\times3^b=5\times3^{-0.857}=5\times0.377\approx1.9$ hours.

Step4: Calculate $b$ for 90% learning rate

For a 90% learning rate, $b=\frac{\ln(0.9)}{\ln(2)}\approx - 0.152$.

For $x = 2$:

$T_2=T_1\times2^b=5\times2^{-0.152}=5\times0.9 = 4.5$ hours.

For $x = 3$:

$T_3=T_1\times3^b=5\times3^{-0.152}=5\times0.837\approx4.2$ hours.

Answer:

For $x = 2$ and 65% LC, it takes 3.3 hours For $x = 3$ and 65% LC, it takes 2.6 hours For $x = 2$ and 55% LC, it takes 2.8 hours For $x = 3$ and 55% LC, it takes 1.9 hours For $x = 2$ and 90% LC, it takes 4.5 hours For $x = 3$ and 90% LC, it takes 4.2 hours