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Given,
Objective function is: Z = 7x + 10y
Constraints are:
x + y ≤ 30000
y ≤ 12000
x ≥ 6000
x, y ≥ 0
x ≥ y
First convert the given inequations into corresponding equations and plot them:
x + y ≤ 30000 → x + y = 30000 (corresponding equation)
Two coordinates required to plot the equation are obtained as:
Put, x = 0 ⇒ y = 30000 (0,30000) - - - - first coordinate. Put, y = 0 ⇒ x = 30000 (30000,0) - - - - second coordinate
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. For a line passing through origin, we put any other coordinate to check the region.
x ≥ y → x - y = 0 (corresponding equation)
Line passing through origin (0,0) and (1,1)
x = 0 is the y - axis and y = 0 is the x - axis
y = 12000 (line parallel to x - axis passing through (0,12000))
x = 6000 (line parallel to x – axis passing through (6000,0))
Hence, we obtain a plot as shown in figure:

The shaded region in the above figure represents the region of feasible solution.
Now to maximize our objective function, we need to find the coordinates of the corner points of the shaded region.
We can determine the coordinates graphically our by solving equations. But choose only those equations to solve which gives one of the corner coordinates of the feasible region.
Solving x + y = 30000 and y = 12000 gives (18000, 12000)
Similarly, solve other combinations by observing graph to get other coordinates.
From figure we have obtained coordinates of corners as:
(18000,12000) , (12000,12000) , (6000,0) , (6000,6000) and (30000,0)