onsider the following linear program. 15 10 (a) Graph the feasible region for the problem. B O Max s.t. 5 14- 28 -44 +38 S3 14-18 ≤ 4 A, B 20 15 10 M 5 A 6 8 10 12 14 2/4 B c) Find the optimal solution. (A, B) = 4,0 2 4 6 8 10 12 14 A B 15 10 DO 5 2 4 (b) Is the feasible region unbounded? Explain. O The feasible region is unbounded because the value of the solution may be made infinitely large without violating any of the constraints. O The feasible region is unbounded because more than one optimal solution occurs without violating any of the constraints. O The feasible region is unbounded because the solution coordinates may be made infinitely large without violating any of the constraints. O The feasible region is unbounded because the value of the solution violates at least one of the constraints. O The feasible region is not unbounded. 68 10 12 14 A B 15 10 2 4 6 8 10 10 12 14 A @

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.3: Systems Of Inequalities
Problem 19E
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Question
Consider the following linear program.
15
10
Max
s.t.
(a) Graph the feasible region for the problem.
B
5
1A 2B
-4A + 3B ≤ 3
1A 1B ≤ 4
A, B 2 0
2 4 6
8
(c) Find the optimal solution.
(A, B) = | 4, 0
10 12 14
A
@O
B
15
10
5
2
4
6
8
10 12 14
A
B
15
10
O
5
2
4
(b) Is the feasible region unbounded? Explain.
O The feasible region is unbounded because the value of the solution may be made infinitely large without violating any of the constraints.
O The feasible region is unbounded because more than one optimal solution occurs without violating any of the constraints.
The feasible region is unbounded because the solution coordinates may be made infinitely large without violating any of the constraints.
O The feasible region is unbounded because the value of the solution violates at least one of the constraints.
O The feasible region is not unbounded.
6
8
10
12
14
A
B
15
10
5
2 /4
6 8
10
12
14
A
Transcribed Image Text:Consider the following linear program. 15 10 Max s.t. (a) Graph the feasible region for the problem. B 5 1A 2B -4A + 3B ≤ 3 1A 1B ≤ 4 A, B 2 0 2 4 6 8 (c) Find the optimal solution. (A, B) = | 4, 0 10 12 14 A @O B 15 10 5 2 4 6 8 10 12 14 A B 15 10 O 5 2 4 (b) Is the feasible region unbounded? Explain. O The feasible region is unbounded because the value of the solution may be made infinitely large without violating any of the constraints. O The feasible region is unbounded because more than one optimal solution occurs without violating any of the constraints. The feasible region is unbounded because the solution coordinates may be made infinitely large without violating any of the constraints. O The feasible region is unbounded because the value of the solution violates at least one of the constraints. O The feasible region is not unbounded. 6 8 10 12 14 A B 15 10 5 2 /4 6 8 10 12 14 A
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