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 ¡Ü 10
3. A + \ 2B ¡Ý 22
4. 3A + 2B - AB = 12
5. 2A2 - 8B ¡Ý 14
Max 2A + 7B
s.t.
A + B ¡Ý 12
2A + 2 B ¡Ü 26
B ¡Ý 1
A, B ¡Ý
the exclamation Y, the symbol is actually greater than or equal to:
A + B greater thanor equal to 12
2A + 2B less than or equal to 26
B greater tha or equal to 1
A, B greater than or equal to
sorry the question goes with the one before this question
To determine whether each mathematical relationship could be found in a linear programming model, we need to understand what constitutes a linear relationship.
Linear relationships are mathematical equations where the variables involved have an exponent of 1 and are not multiplied or divided by each other. In other words, the variables involved are raised to the power of 1 and are added or subtracted together. Linear relationships can also involve inequality signs such as "≤" or "≥".
Now, let's analyze each of the given mathematical relationships and determine whether they fit the criteria for a linear relationship.
1. B-2A + 7B = 45
The equation contains variables (A and B) raised to the power of 1 and added/subtracted together. Therefore, this equation could be found in a linear programming model. The answer is YES.
2. 4A - B ≤ 10
In this equation, variables (A and B) are raised to the power of 1 and subtracted together. Since the variables are not multiplied or divided by each other, and an inequality sign (≤) is used, this equation could be found in a linear programming model. The answer is YES.
3. A + 2B ≥ 22
Similar to the previous equation, this equation contains variables (A and B) raised to the power of 1 and added together. Furthermore, it includes an inequality sign (≥). Therefore, this equation could be found in a linear programming model. The answer is YES.
4. 3A + 2B - AB = 12
In this equation, variable A is multiplied by B (AB). Because the variable A is multiplied by another variable, this equation does not meet the criteria for a linear relationship and could not be found in a linear programming model. The answer is NO.
5. 2A^2 - 8B ≥ 14
In this equation, variable A is raised to the power of 2 (A^2). When a variable is raised to an exponent other than 1, it is not a linear equation. Therefore, this equation does not meet the criteria for a linear relationship and could not be found in a linear programming model. The answer is NO.
To summarize:
1. B-2A + 7B = 45: YES
2. 4A - B ≤ 10: YES
3. A + 2B ≥ 22: YES
4. 3A + 2B - AB = 12: NO
5. 2A^2 - 8B ≥ 14: NO