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Expert: - 9/21/2009


Question
Max 1A - 2B
s.t.
-4A + 3B <= 3
1A - 1B <= 3
A,B => 0

1. graph feasible region
2. is the feasible region unbounded? explain
3. find the optimal solution
4. does an unbounded feasible region imply that the optimal solution to the linear program will be unbounded.


Answer

Linear
Questioner: Jen
Country: United States
Category: Advanced Math
Private: No
Subject: Linear Programming
Question: Max 1A - 2B
s.t.
-4A + 3B <= 3
1A - 1B <= 3
A,B => 0

1. graph feasible region
2. is the feasible region unbounded? explain
3. find the optimal solution
4. does an unbounded feasible region imply that the optimal solution to the linear program will be unbounded.

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Hi, Jen,

Here is what you have to do:

1. Plot the graph of -4x + 3y = 3  (yes, equal)
  Since it says  <=,  y <= ...., so shade below in yellow.

1. Plot the graph of   x - y = 3
  Since it says  -y <=, which is  y >= ..., shade above in blue.

2. blue + yellow = green.  The green is the feasible region.

3. The CORNERS are the possible optimal solutions.  Get the coordinates of each corner and substitute into  1x - 2y.

4. Perhaps.  I don't know.

Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

Education/Credentials
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