The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is approximated by R(x,y) = 18+88x+159y-2x² - 5y²-3xy. Find the number of each that should be sold to produce maximum revenue. Find the maximum revenue. Find the derivatives Rxx, Ryy, and Rxy. Rxx = Ryy=[ Rxy
The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is approximated by R(x,y) = 18+88x+159y-2x² - 5y²-3xy. Find the number of each that should be sold to produce maximum revenue. Find the maximum revenue. Find the derivatives Rxx, Ryy, and Rxy. Rxx = Ryy=[ Rxy
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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| Homework: HW 17.3 |
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![### Calculating Maximum Revenue from Spa and Solar Heater Sales
#### Problem Statement
The total revenue (in hundreds of dollars) from the sale of \( x \) spas and \( y \) solar heaters is approximated by the function:
\[ R(x, y) = 18 + 88x + 159y - 2x^2 - 5y^2 - 3xy \]
Find the number of each that should be sold to produce maximum revenue. Additionally, find the maximum revenue.
#### Task: Find the Derivatives
To find the number of spas (\( x \)) and solar heaters (\( y \)) that should be sold to maximize revenue, we first need to find the second-order partial derivatives.
1. **Second-order partial derivative with respect to \( x \)**:
\[ R_{xx} = \Box \]
2. **Second-order partial derivative with respect to \( y \)**:
\[ R_{yy} = \Box \]
3. **Mixed second-order partial derivative with respect to \( x \) and \( y \)**:
\[ R_{xy} = \Box \]
Fill in the values for \( R_{xx} \), \( R_{yy} \), and \( R_{xy} \):
\[ R_{xx} = \boxed{\phantom{x}}, \quad R_{yy} = \boxed{\phantom{x}}, \quad R_{xy} = \boxed{\phantom{x}} \]
Here, we need to calculate and input the exact values for the second-order derivatives to proceed with determining the critical points and ultimately the maximum revenue.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2eab6076-80d3-498a-8196-b97ae887fd27%2Ff2f13f20-234c-42b6-9fad-e11f25f39bc6%2Fxnn3ek7_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculating Maximum Revenue from Spa and Solar Heater Sales
#### Problem Statement
The total revenue (in hundreds of dollars) from the sale of \( x \) spas and \( y \) solar heaters is approximated by the function:
\[ R(x, y) = 18 + 88x + 159y - 2x^2 - 5y^2 - 3xy \]
Find the number of each that should be sold to produce maximum revenue. Additionally, find the maximum revenue.
#### Task: Find the Derivatives
To find the number of spas (\( x \)) and solar heaters (\( y \)) that should be sold to maximize revenue, we first need to find the second-order partial derivatives.
1. **Second-order partial derivative with respect to \( x \)**:
\[ R_{xx} = \Box \]
2. **Second-order partial derivative with respect to \( y \)**:
\[ R_{yy} = \Box \]
3. **Mixed second-order partial derivative with respect to \( x \) and \( y \)**:
\[ R_{xy} = \Box \]
Fill in the values for \( R_{xx} \), \( R_{yy} \), and \( R_{xy} \):
\[ R_{xx} = \boxed{\phantom{x}}, \quad R_{yy} = \boxed{\phantom{x}}, \quad R_{xy} = \boxed{\phantom{x}} \]
Here, we need to calculate and input the exact values for the second-order derivatives to proceed with determining the critical points and ultimately the maximum revenue.
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