9.8 Using Parentheses

When two or more variables share the same coefficient, i.e. the coefficients have a common divisor, you can factor them out using parentheses. With parentheses the model formulation becomes both simpler and easier to work with.

The parentheses contain decision variables and even full-fledged formulas. Those formulas can, in turn, have more parenthesized expressions, so nested parentheses are allowed. You can enter coefficients in front of the parentheses.

Examples of illegal parentheses:

    1/30 (PrA + 2 PrB)       { = 0.0333 PrA + 0.0666 PrB }
    5 (x + 10 (y + 2z))      { = 5x + 50y + 100z }
    1/(3 + 7) x              { = 0.1 x }

Four main rules apply when you use parentheses. Parenthesized expressions cannot be:

1. Multiplied together.
2. Multiplied by a variable.
3. Used in a denominator if they contain variables.
4. Followed by a coefficient.

These rules ensure that the problem formulation stays linear.

Examples of illegal parentheses:

    (15 + 200)(5x + 3y)      {  Rule 1  }
    (15 + 200) x1            {  Rule 2  }
    1 / (x + 200) Prod1      {  Rule 3  }
    (x + y) / 3              {  Rule 4  }