Consider the following. optimize f(r, p)= 3₁² + rp-p² + p subject to g(r, p) = 3r + 4p = 1 (a) Write the Lagrange system of partial derivative equations. (Enter your answer as a comma-separated list of equations. Use A to represent the Lagrange multiplier.) (b) Locate the optimal point of the constrained system. (Enter an exact number as an integer, fraction, or decimal.) Once you have the answer matrix on the homescreen of your calculator, hit MATH ENTER ENTER to convert any decimal approximations to exact values. Do the same after you've evaluated fat r and p to convert the approximated output value. (r, p, f(r, p)) (c) Identify the optimal point as either a maximum point or a minimum point. O maximum Qminimum
Consider the following. optimize f(r, p)= 3₁² + rp-p² + p subject to g(r, p) = 3r + 4p = 1 (a) Write the Lagrange system of partial derivative equations. (Enter your answer as a comma-separated list of equations. Use A to represent the Lagrange multiplier.) (b) Locate the optimal point of the constrained system. (Enter an exact number as an integer, fraction, or decimal.) Once you have the answer matrix on the homescreen of your calculator, hit MATH ENTER ENTER to convert any decimal approximations to exact values. Do the same after you've evaluated fat r and p to convert the approximated output value. (r, p, f(r, p)) (c) Identify the optimal point as either a maximum point or a minimum point. O maximum Qminimum
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 48CR
Related questions
Question
![**Consider the following:**
\[
\begin{cases}
\text{optimize } f(r, p) = 3r^2 + rp - p^2 + p \\
\text{subject to } g(r, p) = 3r + 4p = 1
\end{cases}
\]
---
### (a) Write the Lagrange system of partial derivative equations.
Enter your answer as a comma-separated list of equations. Use \( \lambda \) to represent the Lagrange multiplier.
\[ \boxed{} \]
---
### (b) Locate the optimal point of the constrained system.
Enter an exact number as an integer, fraction, or decimal.
Once you have the answer matrix on the home screen of your calculator, hit `MATH ENTER ENTER` to convert any decimal approximations to exact values. Do the same after you've evaluated \( f \) at \( r \) and \( p \) to convert the approximated output value to an exact value.
\[ (r, p, f(r, p)) = \left( \boxed{} \right) \]
---
### (c) Identify the optimal point as either a maximum point or a minimum point.
- [ ] maximum
- [ ] minimum](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcfa3f98-eb44-4f4d-86d7-8c297108b84f%2F04b38db6-1e68-4567-9ef2-954753a4ab6d%2F03ag6r_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the following:**
\[
\begin{cases}
\text{optimize } f(r, p) = 3r^2 + rp - p^2 + p \\
\text{subject to } g(r, p) = 3r + 4p = 1
\end{cases}
\]
---
### (a) Write the Lagrange system of partial derivative equations.
Enter your answer as a comma-separated list of equations. Use \( \lambda \) to represent the Lagrange multiplier.
\[ \boxed{} \]
---
### (b) Locate the optimal point of the constrained system.
Enter an exact number as an integer, fraction, or decimal.
Once you have the answer matrix on the home screen of your calculator, hit `MATH ENTER ENTER` to convert any decimal approximations to exact values. Do the same after you've evaluated \( f \) at \( r \) and \( p \) to convert the approximated output value to an exact value.
\[ (r, p, f(r, p)) = \left( \boxed{} \right) \]
---
### (c) Identify the optimal point as either a maximum point or a minimum point.
- [ ] maximum
- [ ] minimum
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