Question

Find the linear inequations for which the solution set is the shaded region given in Fig.

Accepted Answer

First, we consider the line $x + y = 4$ .We observe that shaded region and origin lies on same side of line and $(0,0)$ satisfies $x + y \leq 4$ .
Therefore, we must have $x + y \leq 4$ as the linear inequation corresponding to line $x + y = 4$

Again, we consider the line $x = 3 .$ We observe that shaded region and origin lies on same side of line and $(0,0)$ satisfies the equation $x \leq 3 .$ Therefore we must have $x \leq 3$ as the linear inequation corresponding to line $x = 3$ .

Again, we consider the line $y = 3 .$ We observe that shaded region and origin lies on same side of line and $(0,0)$ satisfies $y \leq 3 .$ Therefore, we must have $y \leq 3$ as the linear inequation corresponding to line $y = 3$

Again, we consider the line $x + 5 y = 4 .$ We observe that shaded region and origin lies on opposite side of line and $(0,0)$ does not satisfy $x + 5 y \geq 4$
Therefore, we must have $x + 5 y \geq 4$ as the linear inequation corresponding to line. $x + 5 y = 4$

Again, we consider the line $6 x + 2 y = 8 .$ We observe that shaded region and origin lies on opposite side of line and $(0,0)$ does not satisfy the equation $6 x + 2 y \geq 8$ $.$ Therefore, we must have $6 x + 2 y \geq 8$ as the linear inequation corresponding to line $6 x + 2 y = 8$ .

Also shaded region is in first quadrant only.
$∴$ We must have $x \geq 0$ and $y \geq 0$

Thus, the linear inequation comprising the given solution set are $x + y \leq 3, 6 x + 2 y \geq 8, x + 5 y \geq 4, x \leq 3, y \leq 3, x \geq 0, y \geq 0$

R D Sharma Solutions for Chapter: Linear Inequations, Exercise 6: EXERCISE 15.6

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Linear Inequations, Exercise 6: EXERCISE 15.6

Questions from R D Sharma Solutions for Chapter: Linear Inequations, Exercise 6: EXERCISE 15.6 with Hints & Solutions

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