# Linear Inequalities and Objective Function Analysis## Objective Function and ConstraintsGiven an objective function and a system of linear inequalities representing constraints, complete the following tasks to analyze the system.### Objective Function\[ z = 4x + 6y \]### Constraints\[\begin{align*}x & \geq 0 \\y & \geq 0 \\2x + y & \leq 14 \\x + y & \geq 7 \\\end{align*}\]## Instructions### a. Graphing the System of InequalitiesGraph the system using the provided graphing tool to visualize the constraints.- Click to enlarge and access the graphing tool. ### b. Calculating Objective Function ValuesFind the value of the objective function $ z $ at each corner of the graphed region.- Use a comma to separate answers as needed.### c. Determining the Maximum ValueUse the values calculated in part (b) to determine the maximum value of the objective function. Identify the values of $ x $ and $ y $ at which this maximum occurs.- The maximum value of the objective function is ______.- Values where the maximum occurs: - $ x = $ ______ - $ y = $ ______**Note:** Click the graph, choose a tool in the palette, and follow the instructions to create your graph.

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Description: # Linear Inequalities and Objective Function Analysis## Objective Function and ConstraintsGiven an objective function and a system of linear inequalities representing constraints, complete the following tasks to analyze the system.### Objective Func

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Answered: 1. Graph the system of inequalities…

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1. Graph the system of inequalities representing the constraints.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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# Linear Inequalities and Objective Function Analysis

## Objective Function and Constraints

Given an objective function and a system of linear inequalities representing constraints, complete the following tasks to analyze the system.

### Objective Function
\[ z = 4x + 6y \]

### Constraints
\[
\begin{align*}
x & \geq 0 \\
y & \geq 0 \\
2x + y & \leq 14 \\
x + y & \geq 7 \\
\end{align*}
\]

## Instructions

### a. Graphing the System of Inequalities
Graph the system using the provided graphing tool to visualize the constraints.

- Click to enlarge and access the graphing tool.

### b. Calculating Objective Function Values
Find the value of the objective function $ z $ at each corner of the graphed region.

- Use a comma to separate answers as needed.

### c. Determining the Maximum Value
Use the values calculated in part (b) to determine the maximum value of the objective function. Identify the values of $ x $ and $ y $ at which this maximum occurs.

- The maximum value of the objective function is ______.
- Values where the maximum occurs:
- $ x = $ ______
- $ y = $ ______

**Note:** Click the graph, choose a tool in the palette, and follow the instructions to create your graph.

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