Solve the linear program using the graphical solution
Not what you're looking for?
(See attached file for full problem description with proper equations and diagrams)
---
Graphical solution procedure
Please help solve this linear problem in the attachment using the graphical solution procedure & graph the feasible region:
Solve the following linear program using the graphical solution procedure:
Max 5x1 + 5x2
s.t.
1x1 < 100
1x2 < 80
2x1 + 4x2 < 400
x1,x2 ≥ 0
Linear programming problem: Graphical Method!
Step 1:
Convert the inequalities into equalities:
1X1 + 0X2 = 100
0X1 + 1X2 = 80
2X1 + 4X2 = 400
Consider the first equation:
1X1 + 0X2 = 100
X1 = 100 and X2 = 0, 1... for all the value of X2, X1=100.
Consider the second equation
0X1¬¬ + 1X2 = 80
X1 = 0 X2 = 80, for all the values of X1¬, X2 = 80.
Consider the third equation
2X1 + 4X2 = 400
X1 = 200 X2¬ = 0
X1 = 0 X2 = 100
Now let us draw the line for the given points, we have
The shaded area in the graph is the solution for the given problem.
We have the boundary points: A(0,0), B(0,80), C(40,80), D(100,50) and E(100,0)
Now we have to plug in the boundary values in objective function,
Max 5X1 + 5X2
A(0,0) = 0
B(0,80) = 400
C(40,80) = 600
D(100,50) = 750
E(100,0) = 500
Since our problem is maximization type, we have to consider point where the objective function attains maximum. In our case 750 is the maximum value and the point is C(100,50) is the point where the objective function attains maximum.
---
Purchase this Solution
Solution Summary
The solution provides detailed and step-by-step instructions, including graphs in the attached Excel file.
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts