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
Which of the above are linear equations?
1-5 the question is asking if these they can be found in a linear programming model? I couldn't use the symbols of greater than or equal to because it makes a weird symbol after I post the question.
What are the answers?
To determine which mathematical relationships could be found in a linear programming model, we need to identify if the given equations or inequalities meet the criteria of a linear function.
1. B-2A + 7B = 45: This equation contains linear terms with variables A and B, as well as a constant term. The variables are raised to the power of 1, and there are no products or divisions involving the variables. Therefore, the equation is linear. The answer is YES.
2. 4A - B ≤ 10: This inequality contains linear terms with variables A and B, and it meets the criteria of a linear inequality. The answer is YES.
3. A + 2B ≥ 22: This inequality contains linear terms with variables A and B and meets the criteria of a linear inequality. The answer is YES.
4. 3A + 2B - AB = 12: This equation contains a product term (AB), which violates the criteria of a linear equation. Therefore, it is not linear. The answer is NO.
5. 2A^2 - 8B ≥ 14: This inequality contains a squared term (A^2), which violates the criteria of a linear inequality. Therefore, it is not linear. The answer is NO.
In summary, the mathematical relationships that could be found in a linear programming model are:
1. YES
2. YES
3. YES
4. NO
5. NO