Chapter 3.9, 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 $\text{Pi}$ be the number of kilns run for 8 hour shift, $\text{Si}$ be the pounds of grade $\text{i}$ sold, $\text{Li}$ be the pounds of grade $\text{i}$ leftover after sales, $\text{NPi}$ be the pounds of grade $\text{i}$ not process, $\text{Pi}$ be the pounds of grade $\text{i}$ produced by kiln that are processed
• LINDO is a software package for linear programming and it helps to get a good feasible solution quickly.
• Hence in this case, the changed formulation of linear problem in LINDO form  is

  $\begin{array}{l}\text{MAX 12 S1 + 14 S2 + 10 S3 + 18 S4 + 20 S5 + 25 S6 - 150 K - 2 P1}\hfill \\ \text{ - P2 - P3 - P4 - 2 P5 - 3 L1 - 2 L2 - 3 L3 - 2 L4 - 4 L5 - 2 L6}\hfill \end{array}$

  Subject to

  $\begin{array}{l}\text{2) 2 K - P1 - NP1 = 0}\hfill \\ \text{ 3) 3 K - P2 - NP2 = 0}\hfill \\ \text{ 4) K - P3 - NP3 = 0}\hfill \\ \text{ 5) 1}\hfill \end{array}$