There are 10 decision variables, x 1 , x 2 , . . . , x 10 , with the following goals:Max 0.067 x 1 + . . . + 0.0590 x 10 Subject to: x 1 + . . . + x 10 &lt; 100 , 000 (Budget)- x 1 ≤ 25 , 000 , . . . , x 10 ≤ 25 , 000 (Divestment Constraint) - x 9 + x 10 ≥ x 1 + . . . + x 4 - x 1 + . . . + x 4 ≤ 50 , 000- x 1 + . . . + x 4 ≥ 20 , 000To fully capture the problem, I have another constraint I'd like to add: each decision variable has to be 0, OR has to be at least 10,000. Is there a good way through a system of inequalities to create this, or should I go backwards and make my decision variables binary to accomplish this?

Question

There are 10 decision variables,       x    1    ,      x    2    ,  .  .  .  ,      x      10  , with the following goals:Max   0.067      x    1    +  .  .  .  +  0.0590      x      10  Subject to:      x    1    +  .  .  .  +      x      10    &amp;lt;  100  ,  000 (Budget)-       x    1    ≤  25  ,  000  ,  .  .  .  ,      x      10    ≤  25  ,  000 (Divestment Constraint) -       x    9    +      x      10    ≥      x    1    +  .  .  .  +      x    4  -       x    1    +  .  .  .  +      x    4    ≤  50  ,  000-       x    1    +  .  .  .  +      x    4    ≥  20  ,  000To fully capture the problem, I have another constraint I&#039;d like to add: each decision variable has to be 0, OR has to be at least 10,000. Is there a good way through a system of inequalities to create this, or should I go backwards and make my decision variables binary to accomplish this?

robegarj · Accepted Answer

Introduce new decision variables y1,...,y10 with the constraints:-       y    1    ,  .  .  .  ,      y      10   are binary decision variables-       x    i    ≥  10  ,  000  ∗      y    i    ,  i  =  1  ,  2  ,  .  .  .  ,  10- Rewrite divestment constraint as       x    i    ≤  25  ,  000  ∗      y    i    ,  i  =  1  ,  2  ,  .  .  .  ,  10

There are 10 decision variables, x 1 </msub> , x 2 </msub> , . .

Answered question

Answer & Explanation

New Questions in Algebra I