Determine the maximum value of $Z=11 x+7 y$ subject to the constraints:
$2 x+y \leq 6, x \leq 2, x \geq 0, y \geq 0$
$2 x+y \leq 6, x \leq 2, x \geq 0, y \geq 0$
(D) We have to maximize $Z=11 x+7 y$ subject to the constraints:
$2 x+y \leq 6$
$x \leq 2$
$x \geq 0, y \geq 0$
The feasible region is bounded by the lines $2x+y=6$,$x=2$,$x=0$,and $y=0$. The corner points of the shaded region are $O(0,0)$,$A(2,0)$,$B(2,2)$,and $C(0,6)$.
Comparing the values of $Z$ at all corner points,the maximum value is $42$ at the point $(0,6)$.
$2 x+y \leq 6$
$x \leq 2$
$x \geq 0, y \geq 0$
The feasible region is bounded by the lines $2x+y=6$,$x=2$,$x=0$,and $y=0$. The corner points of the shaded region are $O(0,0)$,$A(2,0)$,$B(2,2)$,and $C(0,6)$.
| Corner Point | Value of $Z = 11x + 7y$ |
| $O(0,0)$ | $11(0) + 7(0) = 0$ |
| $A(2,0)$ | $11(2) + 7(0) = 22$ |
| $B(2,2)$ | $11(2) + 7(2) = 22 + 14 = 36$ |
| $C(0,6)$ | $11(0) + 7(6) = 42$ |
Comparing the values of $Z$ at all corner points,the maximum value is $42$ at the point $(0,6)$.
Explore More
Similar Questions
The feasible region for an $LPP$ is shown in the figure. Let $z = 3x - 4y$ be the objective function. The minimum value of $Z$ is:
Medium
View SolutionShow that the minimum of $Z$ occurs at more than two points.
Maximize $Z = x + y$,subject to $x - y \leq -1$,$-x + y \leq 0$,$x, y \geq 0$.
Maximize $Z = x + y$,subject to $x - y \leq -1$,$-x + y \leq 0$,$x, y \geq 0$.
Medium
View SolutionCorner points of the feasible region for an $LPP$ are $(0,2), (3,0), (6,0), (6,8)$ and $(0,5)$. Let $Z = 4x + 6y$ be the objective function. The minimum value of $Z$ occurs at
The corner points of the feasible region determined by a system of linear constraints are $(0, 3), (1, 1)$ and $(3, 0)$. If the objective function is $z = px + qy$ where $p, q > 0$, then the condition on $p$ and $q$ such that the minimum of $z$ occurs at both $(3, 0)$ and $(1, 1)$ is . . . . . . .
DifficultMHT CET 2026
View SolutionSolve the Linear Programming Problem graphically:
Minimise $Z = 3x + 5y$
subject to the constraints:
$x + 3y \geq 3$
$x + y \geq 2$
$x, y \geq 0$
Minimise $Z = 3x + 5y$
subject to the constraints:
$x + 3y \geq 3$
$x + y \geq 2$
$x, y \geq 0$
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo