Chapter 3.8, Problem 3P

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 ${\text{x}}_{\text{1}}$ be the dollars invested in bonds, ${\text{x}}_{\text{2}}$ be the dollars invested in home loans, ${\text{ x}}_{\text{3}}$ invested in auto loans and ${\text{x}}_{\text{4}}$ be the dollars invested in personal loans.
• Hence in this case, the linear problem is

  ${\text{Max z = 10x}}_{\text{1}}{\text{+ 16x}}_{\text{2}}{\text{+ 13x}}_{\text{3}}{\text{+ 20x}}_{\text{4}}$

  Subject to

  $\begin{array}{l}{\text{x}}_{\text{1}}{\text{+ x}}_{}\hfill \end{array}$