Chapter 3, Problem 42RP

Explanation of Solution

To minimize the cost of manufacturing the required drugs:

• Assume the following,
  • Let “${\text{P}}_{\text{1}}\text{L}$” be the pounds of drug “1” manufactured in Los Angeles.
  • Let “${\text{P}}_2\text{L}$” be the pounds of drug “2” manufactured in Los Angeles.
  • Let “${\text{P}}_{\text{1}}\text{I}$” be the pounds of drug “1” manufactured in Indianapolis.
  • Let “${\text{P}}_{\text{2}}\text{I}$” be the pounds of drug “2” manufactured in Indianapolis.
  • The objective function to minimize the cost of manufacturing the required drugs is as follows,

  $\text{min z=4}{\text{.1P}}_{\text{1}}{\text{I+4P}}_{\text{1}}\text{L+4}{\text{.5P}}_2\text{I+5}{\text{.2P}}_2\text{L}$

• The above function subject to the following constraints,

  $\begin{array}{l}{\text{P}}_{\text{1}}{\text{L+P}}_{\text{1}}\text{I}\ge 1000\\ {\text{P}}_2{\text{L+P}}_2\text{I}\ge \text{2000}\\ \text{0}{\text{.24P}}_{\text{1}}\text{L+0}{}_{}\end{array}$