Consider the following problem: Maximize -₁ subject to 2x₁ X1 X1, + + X2 x2 2x2 X2, + 2x3 + x3 + x4 + X4 2x3 X4 + x3, - ≥ 6 ≤ 4 X4 ≥ 0. a. Introduce slack variables and draw the requirement space. b. Interpret feasibility in the requirement space. C. You are told that an optimal solution can be obtained by having at most two positive variables while all other variables are set at zero. Utilize this statement and the requirement space to find optimal

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.3: Systems Of Inequalities
Problem 15E
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[1.36] Consider the following problem:
Maximize -₁
subject to 2x₁ +
X1
X1,
x2
x2
+ 2x2
X2,
+ 2x3
+
x3
2x3
x3,
-
+
+++
+
+
X4
X4
x4
X4
≥ 6
≤ 4
≥ 0.
a.
Introduce slack variables and draw the requirement space.
b. Interpret feasibility in the requirement space.
C.
You are told that an optimal solution can be obtained by having at
most two positive variables while all other variables are set at zero.
Utilize this statement and the requirement space to find an optimal
solution.
Transcribed Image Text:[1.36] Consider the following problem: Maximize -₁ subject to 2x₁ + X1 X1, x2 x2 + 2x2 X2, + 2x3 + x3 2x3 x3, - + +++ + + X4 X4 x4 X4 ≥ 6 ≤ 4 ≥ 0. a. Introduce slack variables and draw the requirement space. b. Interpret feasibility in the requirement space. C. You are told that an optimal solution can be obtained by having at most two positive variables while all other variables are set at zero. Utilize this statement and the requirement space to find an optimal solution.
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