Carefully sketch the region of the plane satisfying the system of inequalities. x + 3y < 18 2x + y < 16 x > 0 y 2 0
Carefully sketch the region of the plane satisfying the system of inequalities. x + 3y < 18 2x + y < 16 x > 0 y 2 0
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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![**Problem 9:**
Carefully sketch the region of the plane satisfying the system of inequalities.
\[
\begin{align*}
x + 3y &\leq 18 \\
2x + y &\leq 16 \\
x &\geq 0 \\
y &\geq 0 \\
\end{align*}
\]
**Problem 10:**
A company produces two types of lawn ornaments: gnomes and deer. Each ornament must be fired in a kiln and then painted. Each gnome requires ONE hour in the kiln and TWO hours in the paint department. Each deer requires THREE hours in the kiln and ONE hour in the paint department. The profit from each gnome sold is $10 and the profit from each deer sold is $15. If the kiln is run for a total of EIGHTEEN hours and the paint department is operating for SIXTEEN hours each production cycle, how many gnomes and deer should the company produce to realize the maximum profit? *(Hint: Use the region from Problem 9.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fec9627-716b-4096-bc89-25e30a6ad826%2F6f5a1ee6-2d18-44f3-8935-2f3d2cd4a8a8%2Fw1fspui_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 9:**
Carefully sketch the region of the plane satisfying the system of inequalities.
\[
\begin{align*}
x + 3y &\leq 18 \\
2x + y &\leq 16 \\
x &\geq 0 \\
y &\geq 0 \\
\end{align*}
\]
**Problem 10:**
A company produces two types of lawn ornaments: gnomes and deer. Each ornament must be fired in a kiln and then painted. Each gnome requires ONE hour in the kiln and TWO hours in the paint department. Each deer requires THREE hours in the kiln and ONE hour in the paint department. The profit from each gnome sold is $10 and the profit from each deer sold is $15. If the kiln is run for a total of EIGHTEEN hours and the paint department is operating for SIXTEEN hours each production cycle, how many gnomes and deer should the company produce to realize the maximum profit? *(Hint: Use the region from Problem 9.)*
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