Chapter 3, Problem 28RP

Explanation of Solution

Optimal solution of LP:

To find the optimal solution, follow the steps given below,

Step 1:

Consider each inequality constraint as equality and find 2 pair of points for each of the equations.

Let, $3x_1+x_2=6$

Putting $x_1=0\Rightarrow x_2=6$, the corresponding is, $(0,6)$

Putting $x_2=0\Rightarrow 3x_1=6\Rightarrow x_1=2$, the corresponding is, $(2,0)$

Let, $4x_1+x_2=12$

Putting $x_1=0\Rightarrow x_2=12$, the corresponding is, $(0,12)$

Putting $x_2=0\Rightarrow 4x_1=12\Rightarrow x_1=3$, the corresponding is, $(3,0)$