Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist). (If an answer does not exist, enter DNE.) C = 6x + 8y The x y coordinate plane is given. Four points, three line segments, and a shaded region are on the graph. The shaded region is bounded by the x-axis, the y-axis, and the three line segments. The three line segments connect the following four points in the given order.
Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist). (If an answer does not exist, enter DNE.) C = 6x + 8y The x y coordinate plane is given. Four points, three line segments, and a shaded region are on the graph. The shaded region is bounded by the x-axis, the y-axis, and the three line segments. The three line segments connect the following four points in the given order.
Chapter6: Systems Of Equations And Inequalities
Section6.6: Linear Programming
Problem 50E
Related questions
Question
Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist). (If an answer does not exist, enter DNE.)
C = 6x + 8y
The x y coordinate plane is given. Four points, three line segments, and a shaded region are on the graph. The shaded region is bounded by the x-axis, the y-axis, and the three line segments. The three line segments connect the following four points in the given order.
- (0, 3)
- (4, 4)
- (6, 2)
- (7, 0)
Step 1
We want to find the maximum and minimum values of the objective function
C = 6x + 8y
given the feasible region determined by the constraint inequalities. We know that the optimal values of the objective function will occur at a corner
a corner
of the feasible region. Thus, we need to test the coordinates of the corner points in our objective function.| Corner |
C = 6x + 8y
|
| (0, 0) | 0
0 Excellent job! |
| (7, 0) | 42
42 Nice! |
| (6, 2) | 52
52 Fantastic! |
| (4, 4) | 56
56 Exactly! |
| (0, 3) | 24
24 Nice work! |
Step 2
The maximum value of the objective function is which occurs at
The minimum value of the objective function is which occurs at
(x, y) =
.
The minimum value of the objective function is which occurs at
(x, y) =
.
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