Step - 1

Step - 2

Step - 3

Step - 4

Given,
Objective function is: Z = 3x1 + 4x2
Constraints are:
x1 - x2 ≤ - 1
- x1 + x2 ≤ 0 x1 , x2 ≥ 0
First convert the given inequations into corresponding equations and plot them:
x1 - x2 ≤ - 1 → x1 - x2 = - 1 (corresponding equation)
Two coordinates required to plot the equation are obtained as:
Put, x1 = 0 ⇒ x2 = 1 (0,1) - - - - first coordinate.
Put, x2 = 0 ⇒ x1 = - 1 ( - 1,0) - - - - second coordinate
- x1 + x2 ≤ 0 → - x1 + x2 = 0 (corresponding equation)

Two coordinates required to plot the equation are obtained as:
Put, x1 = 0 ⇒ x2 = 0 (0,0) - - - - first coordinate.
Put, x2 = 1 ⇒ x1 = - 1 ( - 1,1) - - - - second coordinate
x1 ≥ 0 and x2 ≥ 0
Join them to get the line.
As we know, Linear inequation will be a region in the plane, and we observe that the equation divides the XY plane into 2 halves only, so we need to check which region represents the given inequation,
If the given line does not pass through origin then just put (0,0) to check whether inequation is satisfied or not. If it satisfies the inequation origin side is the required region else the other side is the solution.
Similarly, we repeat the steps for other inequation also and find the common region.

Hence, we obtain the following plot:
The given constraints don’t enclose any feasible region. No common shaded region so no maxima exists.