Q. 15 Solve each linear programming pr... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 15 (page 790)

Solve each linear programming problem.
Minimize $z = 5 x + 4 y$ subject to $\{\begin{cases} x 鈮� 0 \\ y 鈮� 0 \\ x + y 鈮� 2 \\ 2 x + 3 y 鈮� 12 \\ 3 x + y 鈮� 12 \end{cases}$

Short Answer

Expert verified

The minimum value is at $8$ at $(0, 2)$

Step by step solution

Step 1. Given information

The given system of linear inequalities is :

$\{\begin{cases} x 鈮� 0 \\ y 鈮� 0 \\ x + y 鈮� 2 \\ 2 x + 3 y 鈮� 12 \\ 3 x + y 鈮� 12 \end{cases}$

The goal of the task is to solve the problem of linear programming. We are looking for the minimum value that can occur if x and y are solutions of the system. We draw a graph of the system and read the corner points from the graph.

Step 2. Draw the graph of the system

Step 3. Make a table for the corner points

Corner point (x,y)	$z = 5 x + 4 y$
$(0, 2)$	$z = 8$
$(0, 4)$	$z = 16$
$(2, 0)$	$z = 10$
$(4, 0)$	$z = 20$
$(\frac{24}{7}, \frac{12}{7})$	$z = 24$

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91影视

Solve each linear programming problem.
Minimize $z = 5 x + 4 y$ subject to $\{\begin{cases} x 鈮� 0 \\ y 鈮� 0 \\ x + y 鈮� 2 \\ 2 x + 3 y 鈮� 12 \\ 3 x + y 鈮� 12 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Draw the graph of the system

Step 3. Make a table for the corner points

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91影视

Solve each linear programming problem.Minimizez=5x+4ysubject tox鈮�0y鈮�0x+y鈮�22x+3y鈮�123x+y鈮�12

Short Answer

Step by step solution

Step 1. Given information

Step 2. Draw the graph of the system

Step 3. Make a table for the corner points

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve each linear programming problem.
Minimize $z = 5 x + 4 y$ subject to $\{\begin{cases} x 鈮� 0 \\ y 鈮� 0 \\ x + y 鈮� 2 \\ 2 x + 3 y 鈮� 12 \\ 3 x + y 鈮� 12 \end{cases}$