A start-up firm has kept careful records of the time required to manufacture itsproduct, a shutoff valve used in gasoline pipelines.Cumulative Number Number of Hours Requiredof Units Produced for Next Unit50 3.3100 2.2400 1.0600 0.81,000 0.510,000 0.2a. Compute the logarithms of the numbers in each column. (Use natural logs.)b. Graph the ln(hours) against the ln(cumulative units) and eyeball a straight-linefit of the data. Using your approximate fit, estimate a and b.c. Using the results of part (b), estimate the time required to produce the first unitand the appropriate percentage learning curve that fits these data.d. Repeat parts (b) and (c), but use an exact least squares fit of the logarithmscomputed in part (a).

A start-up firm has kept careful records of the time required to manufacture its
product, a shutoff valve used in gasoline pipelines.
Cumulative Number Number of Hours Required
of Units Produced for Next Unit
50 3.3
100 2.2
400 1.0
600 0.8
1,000 0.5
10,000 0.2
a. Compute the logarithms of the numbers in each column. (Use natural logs.)
b. Graph the ln(hours) against the ln(cumulative units) and eyeball a straight-line
fit of the data. Using your approximate fit, estimate a and b.
c. Using the results of part (b), estimate the time required to produce the first unit
and the appropriate percentage learning curve that fits these data.
d. Repeat parts (b) and (c), but use an exact least squares fit of the logarithms
computed in part (a).