Solve the following LP problem graphically
MAX 2X + 7Y
Subject to:
5X + 9Y >= 90
9X + 8Y <= 144
Y <= 8
X, Y >= 0
plot y>=10-5/9 x
plot y<=18-9/8 x
plot y<=8
plot x=0
plot y=0
now you have an enclosed area. Test every corner with this function:
value=2x+7y
the corner with the max value is the solution.
or visit
http://www.zweigmedia.com/RealWorld/LPGrapher/lpg.html
and it will show you how it's done
I did one of these for him yesterday.
Oh, forgot the y<8 constraint
To solve the given linear programming problem graphically, let's first plot the feasible region determined by the given constraints.
Step 1: Plot the constraints on a graph
Constraint 1: 5X + 9Y >= 90
To plot this constraint, we can start by rearranging it:
9Y >= 90 - 5X
Y >= (90 - 5X) / 9
We can plot this constraint as the line (90 - 5X) / 9, indicating all the points above this line are feasible.
Constraint 2: 9X + 8Y <= 144
To plot this constraint, we can rearrange it:
8Y <= 144 - 9X
Y <= (144 - 9X) / 8
We can plot this constraint as the line (144 - 9X) / 8, indicating all the points below this line are feasible.
Constraint 3: Y <= 8
This constraint restricts the region below the horizontal line at Y = 8.
Step 2: Find the feasible region
The feasible region is the overlapping area determined by all three constraints.
Step 3: Identify the objective function
The objective function is given as MAX 2X + 7Y. We are looking for the maximum value of this function within the feasible region.
Step 4: Identify the optimal solution
To find the optimal solution, we need to check each corner point of the feasible region and see which one gives the maximum value for the objective function.
Step 5: Calculate the objective function value at each corner point
Evaluate the objective function 2X + 7Y at each corner point of the feasible region.
Step 6: Compare the objective function values
Compare the objective function values at each corner point and determine which one gives the maximum value. That point will be the optimal solution.
By following these steps, you should be able to solve the given linear programming problem graphically.