Chapter 3.8, Problem 12P

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 $\text{G}$ be the fraction of money invested in stocks, $\text{T}$ be the fraction of money invested in T-bills and $\text{G}$ be the fraction of money invested in gold.
• 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

  $\text{MAX 10}\text{.9 S + 16}\text{.9 G + 7}\text{.43 T}$

  Subject to

  $\begin{array}{l}\text{2) 16}\text{.9 S + 26}\hfill \end{array}$