(a) maximize - 4x1 + x2 subject to x1 + x2 ≤2, x1-2x24, x1+x27, x1, x20
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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Can you please give detailed instructions for determining the feasible region graphically in a linear programming problem, I’ve provided a set of questions but I’m not necessarily interested in the answer more so the method etc.
The things I want to understand is:
•Determining which segment (the feasible region) it is in and why
.the perpendicular lines (why are they there and how they should be done, not necessarily the constraints but the directional ones)
•After determining the feasible region, the optimal solution and why that is.
I want to be able to do this myself with great detail and a full understanding, the effort will assist with my studies and is greatly appreciated.
Transcribed Image Text:1. For each of the following linear programs:
(1) Sketch the feasible region of the linear program and the direction of the objec-
tive function.
(2) Use you sketch to find an optimal solution to the program. State the optimal
solution and give the objective value for this solution. If an optimal solution
does not exist, state why.
(a)
maximize
- 4x1 + x2
subject to x1 + x2 ≤2,
-x1+x22,
x1-2x2 <4,
x1+x27,
x1, x20
(b)
maximize x1+2x2
subject to -1+2x2 ≤ 4,
x1 + 3x2 <12,
x1, x20
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