Show the common solution of given inequalities and shade the region bounded by them .
`3x + 2y le 150, x + 4y le 80, x le 15, y ge 0, x ge 0 `

Answer

N/a

Explanation

First inequation : ` 3x + 2y le 150 `
Corresponding equation : ` 3x + 2y = 150 `
This line passes through the points A(50, 0) and B((0, 75). AB.
At point (0, 0), from the inequation, `0le 150` (True)
`:.` The solution of this inequation is that region of XY- plane in which (0, 0) lies.
This line passes thrugh the point C(80, 0) and D(0, 20). Join CD.
At point (0, 0), from the inequation, `0 le 10(True)`
`:.` The solution of this inequation is that region of XY-plane divided by line CD in which (0, 0) lies.
The solution of ` x ge 0, y ge 0 is in first quadrant.
The solution of x`ge` 15 is x = 15 and its left side

`:.` The common solution of given inequations is shown by the shaded region.