Chapter 3, Problem 51RP

Explanation of Solution

LP to minimize the cost of making the required transistors:

• Assume the following,
  • Let “${\text{x}}_1$” be the count of transistors that are melted by method “1”.
  • Let “${\text{x}}_2$”be the count of transistors that are melted by method “1”.
  • Let “D” be the count of defectives that are not refired.
  • Let “DR” be the count of defectives that are refired.
  • Let “${\text{r}}_1$” be the count of grade “1” transistors that are refired.
  • Let “${\text{r}}_2$” be the count of grade “2” transistors that are refired.
  • Let “${\text{r}}_3$” be the count of grade “3” transistors that are refired.
  • Let “${\text{t}}_1$” be the count of grade “1” transistors that are not refired.
  • Let “${\text{t}}_2$” be the count of grade “2” transistors that are not refired.
  • Let “${\text{t}}_3$” be the count of grade “3” transistors that are not refired.
• The Linear Programming (LP) to minimize the cost of making required transistors is as follows,

$\text{Min}{\text{z=50x}}_{\text{1}}{\text{+70x}}_{\text{2}}{\text{+25DR+25r}}_1{\text{+25r}}_2{\text{+25r}}_3$

• The above function subject to the following conditions,
  • “$\text{0}{\text{.3x}}_1+0.2{\text{x}}_2-\text{DR}-\text{D=0}$” denotes the quality of manufactured defective transistor.
  • “$\text{0}{\text{.3x}}_1+0.2{\text{x}}_2-{\text{r}}_1-{\text{t}}_1\text{=0}$” denotes the quality of manufactured grade “1” transistor.
  • “$\text{0}{\text{.2x}}_1+0.25{\text{x}}_2-{\text{r}}_2-{\text{t}}_2\text{=0}$” denotes the quality of manufactured grade “2” transistor