(a) x + y ≤ 16 x + 5y ≤ 20
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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Question
![For the values of \( x \geq 0 \) and \( y \geq 0 \) that maximize \( z = 12x + 13y \), subject to each of the following sets of constraints:
**(a)**
\[
\begin{align*}
x + y & \leq 16 \\
x + 5y & \leq 20 \\
\end{align*}
\]
**(b)**
\[
\begin{align*}
x + 4y & \geq 16 \\
4x + y & \geq 12 \\
x - y & \leq 5 \\
\end{align*}
\]
---
**(a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
- **A.** The maximum value occurs at \(\underline{\hspace{1cm}}\). (Type an ordered pair.)
- **B.** There is no maximum value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3f191a8-a1b2-42ed-ac9e-32d60645d728%2F1a593d8d-4517-4ead-8888-1b9e00413b79%2Fxt6rfrd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For the values of \( x \geq 0 \) and \( y \geq 0 \) that maximize \( z = 12x + 13y \), subject to each of the following sets of constraints:
**(a)**
\[
\begin{align*}
x + y & \leq 16 \\
x + 5y & \leq 20 \\
\end{align*}
\]
**(b)**
\[
\begin{align*}
x + 4y & \geq 16 \\
4x + y & \geq 12 \\
x - y & \leq 5 \\
\end{align*}
\]
---
**(a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
- **A.** The maximum value occurs at \(\underline{\hspace{1cm}}\). (Type an ordered pair.)
- **B.** There is no maximum value.
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