Chapter 3.8, Problem 14P

Explanation of Solution

Formulating a Linear Problem

• The steps for defining a linear problem include:
  • Identifying the decision variables.
  • Writing the objective function.
  • Mentioning the constraints.
  • Explicitly stating the non-negativity restriction.
• A problem will be a linear problem if and only if the decision variables, objective function and constraints all are linear functions.
• If all the three conditions are satisfied, then it is a linear problem.
• Let $\text{RREF}$ be the liters of regular produced, $\text{PREM}$ be the liters of premium produced, $\text{RREF}$ be the liters of reformate used in regular and $\text{PREF}$ be the liters of reformate used in premium.
• LINDO is a software package for linear programming and it helps to get a good feasible solution quickly.
• Hence in this case, the linear problem in LINDO form  is

  $\text{MAX 29}\text{.3625 REG + 31}\text{.3025 PR}$

  Subject to $\begin{array}{l}\text{2) PREF + RREF <= 15572}\hfill \\ \text{3) RFCG + PFCG <= 15434}\hfill \\ \text{4) RISO + PISO <= 6709}\hfill \\ \text{5) RPOL + PPOL <= 1190}\hfill \\ \text{6) RMTB + PMTB\&\#}\hfill \end{array}$