Convert the following problem into an MIP. (Do not optimize) Max. Z = x_{1} + 2x_{2} + 5x_{3} s. t. | - x_{1} + 10x_{2} -3x 3 |>=15 2x_{1} + x_{2} + x_{3} <= 1 x_{1}, x_{2}, x_{3} >= 0
Question
Convert the following problem into an MIP. (Do not optimize) Max. Z = x_{1} + 2x_{2} + 5x_{3} s. t. | - x_{1} + 10x_{2} -3x 3 |>=15 2x_{1} + x_{2} + x_{3} <= 1 x_{1}, x_{2}, x_{3} >= 0
Solution
The given problem can be converted into a Mixed Integer Programming (MIP) problem as follows:
Objective Function: Maximize Z = x_{1} + 2x_{2} + 5x_{3}
Subject to constraints:
The absolute value constraint can be converted into two separate constraints:
-x_{1} + 10x_{2} -3x_{3} >= 15 -x_{1} + 10x_{2} -3x_{3} <= -15
The second constraint remains the same:
2x_{1} + x_{2} + x_{3} <= 1
And the non-negativity constraints:
x_{1}, x_{2}, x_{3} >= 0
This is the MIP formulation of the given problem.
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