Chapter 3.8, Problem 10P

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 $\text{Mi}$ be the tons of coal shipped from mine $\text{i}$ and $\text{xij}$ be the tons of coal shipped from mine $\text{i}$ to customer $\text{j}$.
• 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

  $\begin{array}{l}\text{MIN 50 M1 + 55 M2 + 62 M3 + 4 X11 + 6 X12 + 8 X13 + 12 X14 + 9 X21}\hfill \\ \text{ + 6 X22 + 7 X23 + 11 X24 + 8 X31 + 12 X32 + 3 X33 + 5 X34}\hfill \end{array}$

  Subject to

  $\begin{array}{l}\text{2) M1 <= 120}\hfill \\ \text{3) M2 <= 100}\hfill \\ \text{ 4) M3 <= �}\hfill \end{array}$