Find the linear inequations for which the shaded area in following figure is the solution set:

Options

A. `x+y le 1,2x+ y ge 2,x-2 ge 8,x le 0, y ge 0`
B. `x-y ge 1,2x+y ge2,xge 0, y ge 0`
C. `x-y ge 1,2x+y le 2,x +2y ge 8,x ge 0 ,y ge 0`
D. `x+y ge 1,2 x +y le 2,x +2y ge 8, x ge 0 ,y ge 0`

Answer

C

Explanation

Let ` L_1: x +2y =8, L_2 : 2x +y ge 2, L_3 : x-y =1 `
Since the shaded area is below tha line `L_1`, we have `x+2y le 8` Since . Since. the shaded area is above the line `L_2 ` we have` 2x+y ge 2 ` .Since the common region is to the left of the line ` L_3 ` so we have ` x -y le 1 `