Max 2A + 7B
s.t.
A + B greater than or equal to 12
2A + 2 B less than or equal too 26
B greater than or equal to 1
A, B greater than or equal to
Which of the following would be found in the correct standard form?
A. YES
B. NO
A + B - S1 = 12
2A + 2B - S2 = 26
2A + 2B + S2 = 12
A - S3 = 1
B - S3 = 1
2A + 2B + S2 = 26
The correct standard form for a linear programming problem consists of writing the objective function and constraints in a specific format.
In this case, the objective function is Max 2A + 7B, where A and B are the variables to be optimized.
The constraints are:
1) A + B ≥ 12
2) 2A + 2B ≤ 26
3) B ≥ 1
4) A, B ≥ 0
To put it in standard form, we need to convert the inequalities into equations by introducing slack variables.
The correct standard form for this problem is:
A + B + S1 = 12 (converted from A + B ≥ 12, where S1 is the slack variable)
2A + 2B + S2 = 26 (converted from 2A + 2B ≤ 26, where S2 is the slack variable)
B ≥ 1 (no slack variable needed, as it is already an equation)
A ≥ 0 (no slack variable needed, as it is already an equation)
B ≥ 0 (no slack variable needed, as it is already an equation)
Now, let's compare this with the options given:
A + B - S1 = 12 (not correct, missing the slack variable S1)
2A + 2B - S2 = 26 (correct, matches the second constraint)
2A + 2B + S2 = 12 (not correct, the sign in the right-hand side is incorrect)
A - S3 = 1 (not correct, missing the slack variable S3)
B - S3 = 1 (not correct, missing the slack variable S3)
2A + 2B + S2 = 26 (correct, matches the second constraint)
Therefore, the correct standard form would be found in option B. So the answer is B. NO.