Solve the linear program using the graphical solution
(See attached file for full problem description with proper equations and diagrams)
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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.
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Attachments
Solution Summary
The solution provides detailed and step-by-step instructions, including graphs in the attached Excel file.