### Solving Linear Programming Problem Using Graphical Methods#### Objective:Maximize: $ z = 5x + y $#### Constraints:-$ x - y \leq 11 $ - $ 5x + 3y \leq 75 $ - $ x \geq 0 $ - $ y \geq 0 $ To solve the above linear programming problem graphically, follow these steps:1. **Graphing the Constraints:** - Plot the line $ x - y = 11 $. This can be rewritten as $ y = x - 11 $. - Plot the line $ 5x + 3y = 75 $. This can be rewritten as $ y = \frac{75 - 5x}{3} $.2. **Identifying the Feasible Region:** - Identify and shade the region that satisfies all the constraints simultaneously. This region is known as the feasible region. - Ensure that only the area where both $ x \geq 0 $ and $ y \geq 0 $ is considered, focusing on the first quadrant.3. **Finding the Optimal Solution:** - The optimal solution lies at one of the corner points (vertices) of the feasible region. - Evaluate the objective function $ z = 5x + y $ at each vertex of the feasible region to find the maximum value.#### Graph Description:The image contains a blank graph with a coordinate system. The x-axis and y-axis both range from 0 to 16 and 0 to 26, respectively, with grid lines marking each unit. To create the feasible region:- Calculate the x and y intercepts of each boundary line.- Plot each line by marking intercepts or using the slope-intercept form.- Shade the overlapping region that meets all constraints.Use the graphing tool provided on the right side, labeled “Click to enlarge graph” to plot and illustrate the feasible region clearly.

Answered: Image /qna-images/answer/3bbeeb1d-3371-4b82-bbbe-7c764169e948.jpg

Use graphical methods solve the following linear programming problem. Maximize: z = 5x + y subject to: x-ys 11 5x+3y ≤ 75 x20, y 20 Graph the feasible region using the graphing tool to the right. Click to enlarge graph Ay 26- 24 22 20 18 16 14 12 10 8 6- 4- 14 G

Use graphical methods solve the following linear programming problem. Maximize: z = 5x + y subject to: x-ys 11 5x+3y ≤ 75 x20, y 20 Graph the feasible region using the graphing tool to the right. Click to enlarge graph Ay 26- 24 22 20 18 16 14 12 10 8 6- 4- 14 G

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Solving Linear Programming Problem Using Graphical Methods

#### Objective:
Maximize: $ z = 5x + y $

#### Constraints:
-$ x - y \leq 11 $
- $ 5x + 3y \leq 75 $
- $ x \geq 0 $
- $ y \geq 0 $

To solve the above linear programming problem graphically, follow these steps:

1. **Graphing the Constraints:**
- Plot the line $ x - y = 11 $. This can be rewritten as $ y = x - 11 $.
- Plot the line $ 5x + 3y = 75 $. This can be rewritten as $ y = \frac{75 - 5x}{3} $.

2. **Identifying the Feasible Region:**
- Identify and shade the region that satisfies all the constraints simultaneously. This region is known as the feasible region.
- Ensure that only the area where both $ x \geq 0 $ and $ y \geq 0 $ is considered, focusing on the first quadrant.

3. **Finding the Optimal Solution:**
- The optimal solution lies at one of the corner points (vertices) of the feasible region.
- Evaluate the objective function $ z = 5x + y $ at each vertex of the feasible region to find the maximum value.

#### Graph Description:
The image contains a blank graph with a coordinate system. The x-axis and y-axis both range from 0 to 16 and 0 to 26, respectively, with grid lines marking each unit.

To create the feasible region:
- Calculate the x and y intercepts of each boundary line.
- Plot each line by marking intercepts or using the slope-intercept form.
- Shade the overlapping region that meets all constraints.

Use the graphing tool provided on the right side, labeled “Click to enlarge graph” to plot and illustrate the feasible region clearly.

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