The feasible region (shaded) for a $LPP$ is shown in the adjacent figure. Maximize $Z = 5x + 7y$.
(N/A) The shaded region is bounded by the corner points $O(0,0)$,$A(7,0)$,$B(3,4)$,and $C(0,2)$.
We evaluate the objective function $Z = 5x + 7y$ at each corner point:
Comparing the values of $Z$,the maximum value is $43$,which occurs at the point $B(3,4)$.
We evaluate the objective function $Z = 5x + 7y$ at each corner point:
| Corner Point | Value of $Z = 5x + 7y$ |
|---|---|
| $O(0,0)$ | $5(0) + 7(0) = 0$ |
| $A(7,0)$ | $5(7) + 7(0) = 35$ |
| $B(3,4)$ | $5(3) + 7(4) = 15 + 28 = 43$ |
| $C(0,2)$ | $5(0) + 7(2) = 14$ |
Comparing the values of $Z$,the maximum value is $43$,which occurs at the point $B(3,4)$.
Explore More
Similar Questions
Solve the following problem graphically:
Minimise and Maximise $Z=3x+9y$......$(1)$
subject to the constraints:
$x+3y \leq 60$.....$(2)$
$x+y \geq 10$......$(3)$
$x \leq y$.......$(4)$
$x \geq 0, y \geq 0$......$(5)$
Minimise and Maximise $Z=3x+9y$......$(1)$
subject to the constraints:
$x+3y \leq 60$.....$(2)$
$x+y \geq 10$......$(3)$
$x \leq y$.......$(4)$
$x \geq 0, y \geq 0$......$(5)$
Medium
View SolutionFor the $LP$ problem,minimize $z = 2x + 3y$,the coordinates of the corner points of the bounded feasible region are $A(3, 3), B(20, 3), C(20, 10), D(18, 12),$ and $E(12, 12)$. The minimum value of $z$ is:
Medium
View SolutionThe 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:
Consider the following statements:
Statement $(I)$: In a $LPP$,the objective function is always linear.
Statement $(II)$: In a $LPP$,the linear inequalities on variables are called constraints.
Which of the following is correct?
Statement $(I)$: In a $LPP$,the objective function is always linear.
Statement $(II)$: In a $LPP$,the linear inequalities on variables are called constraints.
Which of the following is correct?
Determine the maximum value of $Z=3x+4y$ if the feasible region (shaded) for a $LPP$ is shown in the adjacent figure.
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