The following five inequalities form the feas | vedclass

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

Question

(C) To identify the redundant constraint,we analyze the feasible region defined by the given inequalities:$1$) $2x - y \leq 8$$2$) $x + y \leq 20$$3$)

Vedclass · Accepted Answer

$-x + y \geq -10$

Vedclass · Answer

(C) To identify the redundant constraint,we analyze the feasible region defined by the given inequalities:$1$) $2x - y \leq 8$$2$) $x + y \leq 20$$3$) $-x + y \geq -10$ (which is $y \geq x - 10$)$4$) $x \geq 0$$5$) $y \geq 0$Consider the constraints $x \geq 0$ and $y \geq 0$. If $x \geq 0$,then $x - 10 \geq -10$. Since $y \geq 0$,the condition $y \geq x - 10$ is automatically satisfied for all $x \geq 0$ and $y \geq 0$ because $y$ is non-negative and $x - 10$ is at most $-10$ when $x=0$. Thus,the constraint $-x + y \geq -10$ does not restrict the feasible region further than the non-negativity constraints $x \geq 0$ and $y \geq 0$. Therefore,$-x + y \geq -10$ is a redundant constraint.

The following five inequalities form the feasible region: $2x - y \leq 8$,$x + y \leq 20$,$-x + y \geq -10$,$x \geq 0$,$y \geq 0$. Which of the following is a redundant constraint?

Similar Questions

The corner points of the feasible region determined by the system of linear constraints are $(2, 72)$,$(15, 20)$,and $(40, 15)$. Let $Z = 6x + 3y$ be the objective function. The minimum value of $Z$ occurs at:

The minimum value of $Z = 2x + 3y$ for the system of linear constraints: $2x + 4y \leq 12$,$x + y \leq 3$,$x \geq 0$,and $y \geq 0$ is . . . . . . .

The corner points of the feasible region determined by the system of linear constraints are $(0,10), (10,15), (15,25), (0,30)$. Let $z = px + qy$,where $p, q > 0$. The condition on $p$ and $q$ so that the maximum of $z$ occurs at both the points $(15,25)$ and $(0,30)$ is . . . . . . .

Solve the following Linear Programming Problem graphically:
Minimise $Z = x + 2y$
subject to the constraints:
$2x + y \geq 3$
$x + 2y \geq 6$
$x, y \geq 0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module