For the linear program

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 the given linear program would be:

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

So, the correct answer would be:

B. NO

To convert the given linear program into standard form, we need to introduce slack variables (S) and rewrite the constraints as equations. The objective function does not need any changes as it is already in the standard form.

The given inequalities are:

A + B ≥ 12 (Constraint 1)
2A + 2B ≤ 26 (Constraint 2)
B ≥ 1 (Constraint 3)
A, B ≥ 0 (Non-negativity constraints)

Let's convert each constraint into equation form:

Constraint 1: A + B - S1 = 12
To convert an inequality into equation form, we introduce a slack variable (S1) and subtract it from the left-hand side to make it equal to 12.

Constraint 2: 2A + 2B + S2 = 26
Again, we introduce a slack variable (S2) and add it to the left-hand side to make it equal to 26.

Constraint 3: B - S3 = 1
Similarly, we introduce a slack variable (S3) and subtract it from B to make it equal to 1.

Finally, the non-negativity constraints remain unchanged:
A, B ≥ 0

Now, let's compare the given options:

Option A: A + B - S1 = 12, 2A + 2B + S2 = 26, A - S3 = 1, B - S3 = 1
This option correctly represents the constraints in standard form.

Option B: 2A + 2B + S2 = 12
This option does not include all the constraints, and it is missing the other two slack variables (S1 and S3).

Therefore, the correct option in standard form is A. YES.