Maximize z=16x + 8y subject to:
2x + y<30
x +2y<24
x>0
y>0
assistance needed
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maximize Z = 30x+50y
subject to
2x+4y=100 and x+5y=80
To maximize the objective function z = 16x + 8y, subject to the given constraints, we can use the graphical method. Here's how:
Step 1: Plot the constraints on a graph:
The first constraint, 2x + y < 30, can be rewritten in slope-intercept form as y < -2x + 30. Plot the line y = -2x + 30 by finding two points on it or by determining the x and y intercepts.
The second constraint, x + 2y < 24, can be rewritten in slope-intercept form as y < -(1/2)x + 12. Plot the line y = -(1/2)x + 12 by finding two points on it or by determining the x and y intercepts.
Step 2: Shade the feasible region:
The feasible region is the region below both lines (since we have '<' inequalities) and restricted by the x>0 and y>0 constraints. Shade this region.
Step 3: Identify the corner points:
The maximum value of the objective function will occur at one of the corner points of the shaded feasible region. Identify the coordinates of all the corner points where the two lines intersect.
Step 4: Evaluate the objective function at each corner point:
Plug the coordinates of each corner point into the objective function z = 16x + 8y to find the corresponding value of z for each point.
Step 5: Determine the maximum value:
The corner point that results in the highest value of z is the maximum value. Compare the values of z at each corner point and select the one with the highest value.
That's it! You have now found the maximum value of z = 16x + 8y subject to the given constraints.