To find the point in the feasible region that maximizes the objective function, we need to evaluate the objective function at each of the corner points of the feasible region.
The corner points of the feasible region can be found by solving the system of equations formed by the constraints.
First, rewriting the constraints in terms of x and y:
1) x >= 0
2) y >= 0
3) -x + 3 >= y
4) y <= (1/3)x + 1
Now, we can graph the feasible region by plotting the following points and lines:
1) (0, 0) - x and y intercepts of the feasible region
2) (3, 0) - intersection of line -x + 3 = y and x = 3
3) (6, 2) - intersection of line y = (1/3)x + 1 and x = 6
4) (0, 1) - intersection of line -x + 3 = y and y = 1
Next, we evaluate the objective function at each corner point:
1) C = 5(0) - 4(0) = 0
2) C = 5(3) - 4(0) = 15
3) C = 5(6) - 4(2) = 22
4) C = 5(0) - 4(1) = -4
From the calculations, we can see that the point (6, 2) maximizes the objective function. So, the point (6, 2) in the feasible region maximizes the objective function.
What point in the feasible region maximizes the objective function ?
The constraints are:
x>=0
y>=0
-x+3>=y
y<=1/3x+1
Object function is:
C=5x-4y
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