The objective function z = 4x + 7y is subject to the constraints 3x + y ≥ 12 x + y ≥ 6 x ≥ 0 and y ≥ 0. Find the following. (If an answer does not exist, enter DNE.) (a) the point at which the maximum occurs (if there is such a point) (x, y) = , (b) the maximum value (c) the point at which the minimum occurs (if there is such a point) (x, y) = , (d) the minimum value
The objective function z = 4x + 7y is subject to the constraints 3x + y ≥ 12 x + y ≥ 6 x ≥ 0 and y ≥ 0. Find the following. (If an answer does not exist, enter DNE.) (a) the point at which the maximum occurs (if there is such a point) (x, y) = , (b) the maximum value (c) the point at which the minimum occurs (if there is such a point) (x, y) = , (d) the minimum value
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The region of possible solutions is not bounded: thus, there may not be both a maximum and a minimum. After graphing the region of possible solutions and finding each corner point, you can determine if both a maximum and a minimum exist by choosing two arbitrary values of z and graphing the corresponding lines, as discussed in the section "Why the Corner Principle Works."
The objective function
z = 4x + 7y
is subject to the constraints
| 3x + y ≥ 12 |
| x + y ≥ 6 |
| x ≥ 0 and y ≥ 0. |
Find the following. (If an answer does not exist, enter DNE.)
(a) the point at which the maximum occurs (if there is such a point)
(x, y) =
,
(b) the maximum value
(c) the point at which the minimum occurs (if there is such a point)
(x, y) =
,
(d) the minimum value
(x, y) =
(b) the maximum value
(c) the point at which the minimum occurs (if there is such a point)
(x, y) =
(d) the minimum value
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