3. The region of experimentation for two factors are temperature (100 ≤T≤300°F) and catalyst feed rate ( 10≤C ≤30 lb/h). A first order model in the usual ± 1 coded variables has been fit to a molecular weight response, yielding the following model. I y=2000+125x₁ + 40x2 (a) Find the path of steepest ascent. (b) It is desired to move to a region where molecular weights are above 2500. Based on the information you have from the experimentation in this region, about how many steps along the path of steepest ascent might be required to move to the region of interest?
3. The region of experimentation for two factors are temperature (100 ≤T≤300°F) and catalyst feed rate ( 10≤C ≤30 lb/h). A first order model in the usual ± 1 coded variables has been fit to a molecular weight response, yielding the following model. I y=2000+125x₁ + 40x2 (a) Find the path of steepest ascent. (b) It is desired to move to a region where molecular weights are above 2500. Based on the information you have from the experimentation in this region, about how many steps along the path of steepest ascent might be required to move to the region of interest?
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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The region of experimentation for two factors are temperature \((100 \leq T \leq 300^\circ F)\) and catalyst feed rate \((10 \leq C \leq 30 \text{ lb/h})\). A first order model in the usual \(\pm 1\) coded variables has been fit to a molecular weight response, yielding the following model.
\[ \hat{y} = 2000 + 125x_1 + 40x_2 \]
(a) Find the path of steepest ascent.
(b) It is desired to move to a region where molecular weights are above 2500. Based on the information you have from the experimentation in this region, about how many steps along the path of steepest ascent might be required to move to the region of interest?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F788dab94-01ba-414a-9745-8d14d9dc9223%2F0b67298d-573f-43f7-8693-fab6e72ed1c0%2F106t7zh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.
The region of experimentation for two factors are temperature \((100 \leq T \leq 300^\circ F)\) and catalyst feed rate \((10 \leq C \leq 30 \text{ lb/h})\). A first order model in the usual \(\pm 1\) coded variables has been fit to a molecular weight response, yielding the following model.
\[ \hat{y} = 2000 + 125x_1 + 40x_2 \]
(a) Find the path of steepest ascent.
(b) It is desired to move to a region where molecular weights are above 2500. Based on the information you have from the experimentation in this region, about how many steps along the path of steepest ascent might be required to move to the region of interest?
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