Construct the region represented by the inequations `x + y ge 4 and 3x + 2y le 6`.

Explanation

(a) We first draw `x+y = 4 rArr y =4 -x`.
`{:(x,,4,,0,,2),(y,,0,,4,,2):}`
Substitute (0, 0) in `x + y ge 4`.
`rArr 0 + 0 ge 4`
`rArr 0 ge4`, which is false.
`therefore` The half plane that does not contain the origin is the graph of `x + y ge 4`.
(d) We draw ` 3x + 2y = 6`.
`{:(x,,0,,2,,4),(y,,3,,0,,-3):}`

Subsitute (0, 0) in `3x + 2y le 6`.
`rArr 3(0) + 2(0) le 6`
`rArr 0 le 6`, which is true.
`therefore ` The origin belongs to the half plane represented by `3x + 2y le 6`.
The region common to the two half planes is the graph of the given system of inequations, which is shown as the shaded region in the given figure.