Question

Given the linear program

MAX 3x+4y
s.t. -x+2y <(or) = 8
x+2y <(or) = 12
2x+y <(or)= 16
x,y >(or)= 0
Write the problem in standard form. Identify slack/surplus
variables.

Answer 1

To convert the given linear program into standard form, multiply the objective function by -1, add slack variables for each constraint, write all variables as nonnegative variables, and remove any surplus variables. The resulting linear program in standard form is: Minimize: -3x - 4y, Subject to: -x + 2y + s1 = 8, 8x + 2y + s2 = 12, 2x + y + s3 = 16, and x, y, s1, s2, s3 ≥ 0. The slack variables introduced are s1, s2, and s3.

Step-by-step explanation:

The given linear program is:

Maximize: 3x + 4y

Subject to:

• -x + 2y ≤ 8
• 8x + 2y ≤ 12
• 2x + y ≤ 16
• x, y ≥ 0

To convert the linear program into standard form, we need to:

1. Convert the objective function to a minimization problem by multiplying it by -1:
2. Add slack variables for each constraint that has ≤ or ≥:
3. Write all variables as nonnegative variables:
4. Remove any surplus variables:

The linear program in standard form is:

Minimize: -3x - 4y

Subject to:

• -x + 2y + s1 = 8
• 8x + 2y + s2 = 12
• 2x + y + s3 = 16
• x, y, s1, s2, s3 ≥ 0

The slack variables introduced are s1, s2, and s3.