Q. 52 In Problems 51 and 52, solve eac... [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. 52 (page 794)

In Problems 51 and 52, solve each linear programming problem.
Minimize $z = 3 x + 5 y$ when $x 鈮� 0; y 鈮� 0; 3 x + 2 y 鈮� 12; x + 3 y 鈮� 12$

Short Answer

Expert verified

By minimizing $z = 3 x + 5 y$ when $x 鈮� 0; y 鈮� 0; 3 x + 2 y 鈮� 12; x + 3 y 鈮� 12$ , the maximum value is $3$ which occurs at $x = 1; y = 0$

Step by step solution

Step 1. Given

The problem:

$z = 3 x + 5 y$

The constraints:

$x 鈮� 0; y 鈮� 0; 3 x + 2 y 鈮� 12; x + 3 y 鈮� 12$

Step 2. Graph the constraints.

The graph of the constraints (the feasible points) is illustrated:

Step 3. List the corner points

We list the corner points and evaluate the objective function at each.

S.No.	Corner points(x, y)	Value of the objective function $z = 3 x + 5 y$
1.	$(1, 0)$	$z = 3 (1) + 5 (0) = 3$
2.	$(4, 0)$	$z = 3 (4) + 5 (0) = 12$
3.	$(1.71, 3.43)$	$z = 3 (1.71) + 5 (3.43) = 22.1$
4.	$(0, 4)$	$z = 3 (0) + 5 (4) = 20$
5.	$(0, 1)$	$z = 3 (0) + 5 (1) = 5$

Step 4. Minimize the objective function.

From the table, the minimum value of the given objective function is $3$ and it occurs at $x = 1; y = 0$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In Problems 51 and 52, solve each linear programming problem.
Minimize $z = 3 x + 5 y$ when $x 鈮� 0; y 鈮� 0; 3 x + 2 y 鈮� 12; x + 3 y 鈮� 12$

Short Answer

Step by step solution

Step 1. Given

Step 2. Graph the constraints.

Step 3. List the corner points

Step 4. Minimize the objective function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Decision Maths

Statistics

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

91影视

In Problems 51 and 52, solve each linear programming problem.Minimizez=3x+5y when x鈮�0;y鈮�0;3x+2y鈮�12;x+3y鈮�12

Short Answer

Step by step solution

Step 1. Given

Step 2. Graph the constraints.

Step 3. List the corner points

Step 4. Minimize the objective function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Decision Maths

Statistics

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 51 and 52, solve each linear programming problem.
Minimize $z = 3 x + 5 y$ when $x 鈮� 0; y 鈮� 0; 3 x + 2 y 鈮� 12; x + 3 y 鈮� 12$