The feasible region represented by the given | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) To find the feasible region,we analyze the given constraints:$1$. $2x + 3y \geqslant 12$: The region is on or above the line $2x + 3y = 12$.$2$. $

Vedclass · Accepted Answer

$S_4$

Vedclass · Answer

(D) To find the feasible region,we analyze the given constraints:$1$. $2x + 3y \geqslant 12$: The region is on or above the line $2x + 3y = 12$.$2$. $-x + y \leqslant 3$: The region is on or below the line $-x + y = 3$.$3$. $x \leqslant 4$: The region is to the left of the line $x = 4$.$4$. $y \geqslant 3$: The region is on or above the line $y = 3$.By observing the graph and testing the constraints:- The region $S_1$ is above $y=3$,to the left of $x=4$,above $2x+3y=12$,and above $-x+y=3$. This does not satisfy the constraints.- The region $S_4$ is bounded by $y=3$,$x=4$,$-x+y=3$,and $2x+3y=12$. Checking a point in $S_4$,say $(1, 4)$:- $2(1) + 3(4) = 14 \geqslant 12$ (True)- $-(1) + 4 = 3 \leqslant 3$ (True)- $1 \leqslant 4$ (True)- $4 \geqslant 3$ (True)All constraints are satisfied in region $S_4$.

The feasible region represented by the given constraints $2x + 3y \geqslant 12$,$-x + y \leqslant 3$,$x \leqslant 4$,$y \geqslant 3$ is denoted by

Similar Questions

The maximum value of the objective function $Z = 3x + 2y$ for the linear constraints $x + y \leq 7$,$2x + 3y \leq 16$,$x \geq 0$,$y \geq 0$ is

The objective function $z=x_1+x_2$,subject to $x_1+x_2 \leq 10, -2x_1+3x_2 \leq 15, x_1 \leq 6, x_1, x_2 \geq 0$,has a maximum value at:

The maximum value of $z=7x+8y$ subject to the constraints $x+y \leq 20, y \geq 5, x \leq 10, x \geq 0, y \geq 0$ is

For the following shaded region,the linear constraints are:

The graphical solution set of the system of inequations $x+y \geq 1$,$7x+9y \leq 63$,$y \leq 5$,$x \leq 6$,$x \geq 0$,$y \geq 0$ is represented by:

Vedclass Test Series

Exam Paper Generator

Online Exam Module