Chapter 3.9, Problem 9P

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 $\text{A}$ be the pounds of raw material used to produce input $\text{ i}$ where $\text{ i}$ = 1, 2, $\text{Pi}$ be the times process $\text{ i}$ is run, $\text{Li}$ be the ounces of input $\text{ i}$ leftover, $\text{iS}$ be the ounces sold of product $\text{ i}$ where $\text{ i}$ = $\text{A}$, $\text{C}$ be the ounces of $\text{C}$ sold, $\text{D}$ be the ounces of $\text{D}$ sold , $\text{WD}$ be the ounces of waste disposed of in river, $\text{RM}$ be the pounds of raw material purchased, $\text{LA}$ be the ounces of product $\text{A}$ leftover and $\text{LB}$ be the ounces of product $\text{B}$ leftover.
• LINDO is a software package for linear programming and it helps to get a good feasible solution quickly