Chapter 3, Problem 10RP

Explanation of Solution

To maximize the number of new customers:

• Assume the following,
  • Let “${\text{a}}_1$” be the number of newspaper advertisements creating “900” customers.
  • Let “${\text{a}}_2$” be the number of newspaper advertisements creating “600” customers.
  • Let “${\text{a}}_3$” be the number of newspaper advertisements creating “300” customers.
  • Let “${\text{a}}_4$” be the number of Television (TV) advertisements creating “10000” customers.
  • Let “${\text{a}}_5$” be the number of TV advertisements creating “5000” customers.
  • Let “${\text{a}}_6$” be the number of TV advertisements creating “2000” customers.
• The objective function that maximizes the number of new customers is as follows,

  $\text{max}{\text{z=900a}}_{\text{1}}{\text{+600a}}_{\text{2}}{\text{+300a}}_{\text{3}}{\text{+10000a}}_{\text{4}}{\text{+5000a}}_{\text{5}}{\text{+2000a}}_{\text{6}}$

  $\begin{array}{l}\text{S}\text{.T}\text{.}\\ {\text{a}}_{\text{1}}+{\text{a}}_2+{\text{a}}_3\le 30\\ {\text{a}}_4+{\text{a}}_5+{\text{a}}_6\le 15\\ {\text{a}}_1+{\text{a}}_2+{\text{a}}_3{\text{+10a}}_4+10{\text{a}}_5+10{\text{a}}_6\le 150\\ {\text{a}}_1\le 10\\ {\text{a}}_{}\end{array}$