Optimización y simulación [DOI-IMAT-314] Course Materials & Test Answers | sifo.comillas.edu

Consider

the following optimization linear program:

$\text{max} 2x_{1}+x_{2}+4x_{3}$ \text{max} 2x_{1}+x_{2}+4x_{3}

$5x_{1}+3x_{2}+x_{3} \geq 450$ 5x_{1}+3x_{2}+x_{3} \geq 450

$7x_{1}+5x_{2}+2x_{3} \geq 350$ 7x_{1}+5x_{2}+2x_{3} \geq 350

$3x_{1}+2x_{2}+x_{3} \leq 400$ 3x_{1}+2x_{2}+x_{3} \leq 400

$x_{1},x_{2},x_{3} \geq 0$ x_{1},x_{2},x_{3} \geq 0

Given the following information about the

optimal solution of this problem,

as a maximization problem, where $e_{1}, e_{2}, h_{3}$ e_{1}, e_{2}, h_{3} are the

slack/excess variables of the first, second and

third constraint respectively:

Select the correct answer:

If we increase the right-hand-side value of the

second constraint in one unit (from 350 to 351) the objective function

decreases in two units.

None of the other options are correct.

If we increase the right-hand-side value of the

first constraint in one unit (from 450 to 451) the objective function increases

in ten units.

If we increase the right-hand-side value of the

third constraint in one unit (from 400 to 401) the objective function increases

in nine units.

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