Prepare a graph of the constraints and objective function and solve the following linear programming problem: Maximize: f=2x₁-x₂ Subject to constraint 1: x₁ + x₂ > 2 constraint 2: x₁ + x₂ ≤5 constraint 3: x₁-x₂ ≤1 constraint 4: -x₁ + x₂ ≤4 constraint 5: x, 20 constraint 6: x₂ 20 Hints: Draw the line of each constraint on the graph below (two constraints are already drawn) After drawing all the lines shade the optimal region. Try f-0, f=2 and f-4. Which one is the optimum, and what are the values of x1 and x2? -B constraint2 -2 -1 -5 --4- 3- 2- 1 +0 -1- -2 --3- -4 X₂ 0 constraint4 1 2 3 4 5 X 6 x₂

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Prepare a graph of the constraints and objective function and solve the following linear programming
problem:
Maximize:
f=2x₁-x₂
Subject to
constraint 1: x₁ + x₂ > 2
constraint 2: x₁ + x₂ ≤5
constraint 3: x₁-x₂ ≤1
constraint 4: -x₁ + x₂ ≤4
constraint 5: x, 20
constraint 6: x₂ 20
Hints:
Draw the line of each constraint on the graph below (two constraints are already drawn)
After drawing all the lines shade the optimal region.
Try f-0, f=2 and f-4. Which one is the optimum, and what are the values of x₁ and x2?
-B
constraint2
-2
-1
-5
--4-
3-
2-
1
+0
-1-
-2
--3-
X₂
0
constraint4
1
2
3
4
5 X
6
X₁
Transcribed Image Text:Prepare a graph of the constraints and objective function and solve the following linear programming problem: Maximize: f=2x₁-x₂ Subject to constraint 1: x₁ + x₂ > 2 constraint 2: x₁ + x₂ ≤5 constraint 3: x₁-x₂ ≤1 constraint 4: -x₁ + x₂ ≤4 constraint 5: x, 20 constraint 6: x₂ 20 Hints: Draw the line of each constraint on the graph below (two constraints are already drawn) After drawing all the lines shade the optimal region. Try f-0, f=2 and f-4. Which one is the optimum, and what are the values of x₁ and x2? -B constraint2 -2 -1 -5 --4- 3- 2- 1 +0 -1- -2 --3- X₂ 0 constraint4 1 2 3 4 5 X 6 X₁
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