Consider the following linear programming problem Мax .03С .04N s.t. > 30,000 > 10,000 .25 C .20 N .25 C .40 N 4 C 6 N s 1,200,000 C, N, 2 0 a. Write the problem in standard form. b. Use a graph to show each constraint and the feasible region. c. Identify the optimal solution point on your graph. What are the values of C and N at the optimal solution? d. What is the optimal value of the objective function? e. What are the values of slack and surplus variables at the optimal solution?
Consider the following linear programming problem Мax .03С .04N s.t. > 30,000 > 10,000 .25 C .20 N .25 C .40 N 4 C 6 N s 1,200,000 C, N, 2 0 a. Write the problem in standard form. b. Use a graph to show each constraint and the feasible region. c. Identify the optimal solution point on your graph. What are the values of C and N at the optimal solution? d. What is the optimal value of the objective function? e. What are the values of slack and surplus variables at the optimal solution?
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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![**Assignment: A Maximization Problem**
Consider the following linear programming problem:
**Maximize:**
\[
0.03C + 0.04N
\]
**Subject to:**
\[
\begin{align*}
0.25C & \geq 30,000 \\
0.20N & \geq 10,000 \\
0.25C - 0.40N & \geq 0 \\
4C + 6N & \leq 1,200,000 \\
C, N & \geq 0 \\
\end{align*}
\]
**Tasks:**
a. Write the problem in standard form.
b. Use a graph to show each constraint and the feasible region.
c. Identify the optimal solution point on your graph. What are the values of \(C\) and \(N\) at the optimal solution?
d. What is the optimal value of the objective function?
e. What are the values of slack and surplus variables at the optimal solution?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fa0ba7d-b59b-4292-8eda-83dce31ac2cd%2F664d2084-dc91-4cb7-9e67-663cd5131ddf%2Flgoq87c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Assignment: A Maximization Problem**
Consider the following linear programming problem:
**Maximize:**
\[
0.03C + 0.04N
\]
**Subject to:**
\[
\begin{align*}
0.25C & \geq 30,000 \\
0.20N & \geq 10,000 \\
0.25C - 0.40N & \geq 0 \\
4C + 6N & \leq 1,200,000 \\
C, N & \geq 0 \\
\end{align*}
\]
**Tasks:**
a. Write the problem in standard form.
b. Use a graph to show each constraint and the feasible region.
c. Identify the optimal solution point on your graph. What are the values of \(C\) and \(N\) at the optimal solution?
d. What is the optimal value of the objective function?
e. What are the values of slack and surplus variables at the optimal solution?
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