Chapter 3, Problem 59RP

a.

Explanation of Solution

LP to solve the given problem:

• Let “${\text{R}}_{\text{t}}$” be the resistance of resistor “t”.
• The Linear Programming (LP) to solve the given problem is as follows,

$\text{Min}{\text{z=16R}}_1{\text{+36R}}_2{\text{+64R}}_3{\text{+324R}}_4$

• The above function subject to the following conditions,
  • “${\text{4R}}_1{\text{=6R}}_2$” (Given ${\text{V}}_{\text{1}}={\text{V}}_2={\text{V}}_3$)
  • “

b.

Explanation of Solution

LP to solve the given problem:

• Let “${\text{R}}_{\text{j}}\text{'}$” be the reciprocal of “${\text{R}}_{\text{j}}$”, where “${\text{R}}_{\text{j}}$” is resistance of resistor “j”.
• The Linear Programming (LP) to solve the given problem is as follows,

$\text{Min}{\text{z=36R}}_1{\text{'+36R}}_2{\text{'+36R}}_3{\text{'+16R}}_4\text{'}$

• The above function subject to the following conditions,
  • “${\text{6R}}_1{\text{'+6R}}_2{\text{'+6R}}_3{\text{'=4R}}_4\text{'}$” (Given ${\text{I}}_{\text{1}}{\text{+I}}_{\text{2}}{\text{+I}}_{}$