The function to be maximized is given by Z=2x | vedclass

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

Question

(B) The feasible region is bounded by the lines $x+y=5$,$4x+3y=24$,$x=0$,and $y=0$. To find the corner points,we identify the vertices of the shaded r

Vedclass · Accepted Answer

$12, (6,0)$

Vedclass · Answer

(B) The feasible region is bounded by the lines $x+y=5$,$4x+3y=24$,$x=0$,and $y=0$. To find the corner points,we identify the vertices of the shaded region: $1$. The intersection of $x=0$ and $4x+3y=24$ gives $(0, 8)$. $2$. The intersection of $x=0$ and $x+y=5$ gives $(0, 5)$. $3$. The intersection of $x+y=5$ and $4x+3y=24$ is found by solving the system: $y=5-x \implies 4x+3(5-x)=24 \implies x=9, y=-4$ (Not in the first quadrant). Looking at the graph,the vertices are $(0, 5)$,$(0, 8)$,and the intersection of $4x+3y=24$ with the $x$-axis $(6, 0)$ and $x+y=5$ with the $x$-axis $(5, 0)$. Evaluating $Z=2x+y$ at the corner points: At $(0, 5)$,$Z = 2(0) + 5 = 5$. At $(0, 8)$,$Z = 2(0) + 8 = 8$. At $(5, 0)$,$Z = 2(5) + 0 = 10$. At $(6, 0)$,$Z = 2(6) + 0 = 12$. The maximum value is $12$ at the point $(6, 0)$.

The function to be maximized is given by $Z=2x+y$. The feasible region for this function $Z$ is the shaded region shown in the figure. The maximum value of $Z$ is . . . . . . and occurs at the point . . . . . . .

Similar Questions

The correct constraints for the given feasible region are:

The shaded part of the given figure indicates the feasible region. Then the constraints are

Minimize the objective function $Z = 3x + 2y$ subject to the constraints: $x + y \geq 8$,$x + y \leq 5$,$x \geq 0$,$y \geq 0$.

The minimum value of the objective function $Z = 5x + 8y$,subject to the constraints $x + y \geq 5$,$x \leq 4$,$y \leq 2$,$x \geq 0$,and $y \geq 0$,occurs at the point:

The solution set of the constraints $2x + 3y \leq 6$,$x + 4y \leq 4$,$x \geq 0$,and $y \geq 0$ includes the point $\ldots$ as a corner point.

Vedclass Test Series

Exam Paper Generator

Online Exam Module