Find the linear constraints for which the shaded area in the figure below is the solution set.

Explanation

Consider the line `3x+y=18.`
Clearly, O(0,0) satisfies `3x +4y le18.`
Clearly, the shaded area and (0,0) lie on the same side of the line `3x+4y=18.`
So, we must have `3x+4y le18.`
Consider the line `x-6y=3.`
Clearly, (0,0)satisfies the inequation `x-6y le3.`
Also, the shaded are and (0,0) lie on the same side of the line `x-6y=3.`
So, we must have `x-6y le3.`
Consider the line `2x+3y=3.`
Clearly, (0,0) satisfies the inequation `2x+3yle3.`
But th shaded region and the point (0,0) lie on the opposite sides of the line `2x+3y =3.`
So, we must have `2x+3y ge3.`
Consider the line `-7x +14y=14.`
Clearly, (0,0) satisfies the inequation `-7x+14yle14.`
Also the shaded region and the point (0,0) lie on the same side of the line `-7x+14yle14.`
So we must have `-7x+14y=14.`
The shaded region is above the x-axis and on the right-hand side of the y-axis, so we have `y ge0and x ge 0.`
Thus, the linear constraints for which the shaded area in the given figure is the solution set, are
`3x+4yle18mx-6yle3,2x+3yge3,`
`-7x+14yle14,xge0and y ge0.`