Hint:Solve the below formulated LPM using Graphics method.
Z-Min = 1500x+2400y
Subjected to:
4x+Y>24
2x+3y>42
X+4y>36
X<14
Y<14
X, y>0 Required: Perform the below requirements by Using the Graphics method through considering
appropriate steps and procedures.
i. Solve using Graphics method?
Question:
Hint: Solve the below formulated LPM using Graphics method.
Z-Min = 1500x+2400y
Subjected to:
4x+Y>24
2x+3y>42
X+4y>36
X<14
Y<14
X, y>0 Required: Perform the below requirements by Using the Graphics method through considering
appropriate steps and procedures.
i. Solve using Graphics method?
Solution:
Step 1:
I will consider x as the x-axis on the graph and the y as the y-axis on the graph. Every constrain will treated as a linear equation and plotted in the graph. Then I will use the appropriate inequality conditions to mark the feasibility area solutions.
The first constraint 4x + Y > 24, is considered as the equation.
4x + Y = 24
This indicates that on plotting the equation on a graph, the x will cut the x-axis at 6 and the y cuts y-axis at 24, forming a straight line.
Similarly, the other constraints:
2x + 3y > 42 considered equation 2x + 3y = 42
The x-axis = 21 and y-axis = 14
X + 4y > 36 considered equation X + 4y = 36
The x-axis = 36 and y-axis = 9
X < 14 considered equation X = 14
The x-axis = 14 and y-axis = 0
Y < 14 considered equation Y = 14
The x-axis = 0 and y-axis = 14
Step 2:
Determining the coordinates of the extreme points.
Extreme Point Coordinate
O (0, 0)
A (9. 0)
B (8, 4)
C (0, 6)
Step 3:
In this step, we evaluate the value of the objective at every extreme point.
Extreme Point Coordinate (X, Y) Objective Functional Value
Z = 1500x + 2400y
O (0, 0) 1500(0) + 2400(0) = 0
A (9. 0) 1500(9) + 2400(0) = 13500
B (8, 4) 1500(8) + 2400(4) = 21600
C (0, 6) 1500(0) + 2400(6) = 14400
Step 4:
Determine the optimal value of the function.
From Step 3 above, the maximum value of the objective function. The maximum value of Z = 21600and is achieved at vertex B (8, 4). Thus, the optimal solution is given by
Answer:
X = 8
Y = 4
Objective function value = 21600
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