For the linear program

Max 2A + 7B

s.t.

A + B ¡Ý 12

2A + 2 B ¡Ü 26

B ¡Ý 1

A, B ¡Ý



Which of the following would be found in the correct standard form?

A + B - S1 = 12
2A + 2B - S2 = 26
2A + 2B + S2 = 12
A - S3 = 1
B - S3 = 1
2A + 2B + S2 = 26

To convert the given linear program to standard form, we need to rewrite all the inequality constraints as equality constraints and introduce slack or surplus variables.

The original problem:
Max 2A + 7B
s.t.
A + B ≥ 12
2A + 2B ≤ 26
B ≥ 1
A, B ≥ 0

First, let's rewrite the inequality constraints as equality constraints:
A + B = 12 (we introduce a slack variable S1)
2A + 2B = 26 (we introduce a surplus variable S2)
B = 1 (no need to introduce an additional variable for this constraint)

So, the new set of equations becomes:
A + B + S1 = 12
2A + 2B - S2 = 26
B = 1

Now, to put the problem in standard form, we need to express all variables on the left-hand side of the equations. To achieve this, we can rewrite the equations as follows:

A + B - S1 = 12
2A + 2B + S2 = 26
B - 1 = 0

Therefore, the correct standard form for the given linear program is:
A + B - S1 = 12
2A + 2B + S2 = 26
B - S3 = 1

So, none of the options provided in the question matches the correct standard form.