Which of the following mathematical relationships could be found in a linear programming model? Choose YES if the relationship could be, and NO if it could not.
A. YES
B. NO
1. B-2A + 7B = 45
2. 4A - B less than or equal to 10
3. A + \ 2B greater than or equal to 22
4. 3A + 2B - AB = 12
5. 2A2 - 8B greater than or equal to 14
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Sra
how do I solve the following linear programming model graphically usin QM:
Minimize Z= 8x1 + 6x2
Subject to 4x1 + 2x2 < 20
-6x1 +4x2 < 12
X1 + x2 < 6
X1,X2 > 0
To determine which of the mathematical relationships could be found in a linear programming model, we need to understand the characteristics of a linear programming model.
A linear programming model involves optimizing an objective function subject to a set of linear constraints. In other words, it seeks to maximize or minimize a linear equation while fulfilling certain linear inequalities or equalities.
Let's analyze each of the given relationships:
1. B-2A + 7B = 45
This equation contains linear terms (B and A) and constant terms, with addition and subtraction operations. Therefore, it can be a part of a linear programming model. The answer is YES.
2. 4A - B ≤ 10
In a linear programming model, the constraints are typically in the form of inequalities. Here, we have a linear inequality. The answer is YES.
3. A + 2B ≥ 22
Similar to the previous equation, this relationship represents a linear inequality. Hence, it can be found in a linear programming model. The answer is YES.
4. 3A + 2B - AB = 12
Although this equation contains linear terms (A and B), it also includes a non-linear term (AB). In linear programming models, the relationships are restricted to linear equations and inequalities. Therefore, this equation cannot be found in a linear programming model. The answer is NO.
5. 2A^2 - 8B ≥ 14
The term A^2 in this equation is a non-linear term, which violates the linearity required in linear programming models. Hence, this relationship cannot exist in a linear programming model. The answer is NO.
In summary:
1. YES
2. YES
3. YES
4. NO
5. NO