(a) maximize - 4x1 + x2 subject to x1 + x2 ≤2, x1-2x24, x1+x27, x1, x20

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 15E
icon
Related questions
Question
Can you please give detailed instructions for determining the feasible region graphically in a linear programming problem, I’ve provided a set of questions but I’m not necessarily interested in the answer more so the method etc. The things I want to understand is: •Determining which segment (the feasible region) it is in and why .the perpendicular lines (why are they there and how they should be done, not necessarily the constraints but the directional ones) •After determining the feasible region, the optimal solution and why that is. I want to be able to do this myself with great detail and a full understanding, the effort will assist with my studies and is greatly appreciated.
1. For each of the following linear programs:
(1) Sketch the feasible region of the linear program and the direction of the objec-
tive function.
(2) Use you sketch to find an optimal solution to the program. State the optimal
solution and give the objective value for this solution. If an optimal solution
does not exist, state why.
(a)
maximize
- 4x1 + x2
subject to x1 + x2 ≤2,
-x1+x22,
x1-2x2 <4,
x1+x27,
x1, x20
(b)
maximize x1+2x2
subject to -1+2x2 ≤ 4,
x1 + 3x2 <12,
x1, x20
Transcribed Image Text:1. For each of the following linear programs: (1) Sketch the feasible region of the linear program and the direction of the objec- tive function. (2) Use you sketch to find an optimal solution to the program. State the optimal solution and give the objective value for this solution. If an optimal solution does not exist, state why. (a) maximize - 4x1 + x2 subject to x1 + x2 ≤2, -x1+x22, x1-2x2 <4, x1+x27, x1, x20 (b) maximize x1+2x2 subject to -1+2x2 ≤ 4, x1 + 3x2 <12, x1, x20
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill