33. 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 10,000 0.5 0.2 a. Compute the logarithms of the numbers in each column. (Use natural logs.) b. Graph the In(hours) against the In(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).
33. 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 10,000 0.5 0.2 a. Compute the logarithms of the numbers in each column. (Use natural logs.) b. Graph the In(hours) against the In(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).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:33. 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
of Units Produced
Number of Hours Required
for Next Unit
50
3.3
100
2.2
400
1.0
600
0.8
1,000
10,000
0.5
0.2
a. Compute the logarithms of the numbers in each column. (Use natural logs.)
b. Graph the In(hours) against the In(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).
Expert Solution
Step 1
Given that
| Cumulative number of units produced() | Number of hours required for next unit(h()) |
| 50 | 3.3 |
| 100 | 2.2 |
| 400 | 1.0 |
| 600 | 0.8 |
| 1000 | 0.5 |
| 10000 | 0.2 |
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