The feasible region of the L.P.P. (Linear Pro | vedclass

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

Question

(D) To find the feasible region,we first determine the intercepts of the boundary lines:$	ext{Line}$$	ext{Intercepts}$$8x + 5y = 60$$A(7.5, 0), B(0,

Vedclass · Accepted Answer

a quadrilateral

Vedclass · Answer

(D) To find the feasible region,we first determine the intercepts of the boundary lines:$	ext{Line}$$	ext{Intercepts}$$8x + 5y = 60$$A(7.5, 0), B(0, 12)$$4x + 5y = 40$$C(10, 0), D(0, 8)$Solving the equations $8x + 5y = 60$ and $4x + 5y = 40$ simultaneously:Subtracting the second from the first: $(8x - 4x) = 60 - 40 \Rightarrow 4x = 20 \Rightarrow x = 5$.Substituting $x = 5$ into $4x + 5y = 40$: $4(5) + 5y = 40 \Rightarrow 20 + 5y = 40 \Rightarrow 5y = 20 \Rightarrow y = 4$.So,the intersection point is $E(5, 4)$.The constraints $x \geq 0, y \geq 0$ restrict the region to the first quadrant.The feasible region is bounded by the vertices $O(0, 0)$,$A(7.5, 0)$,$E(5, 4)$,and $D(0, 8)$.Since there are four vertices,the feasible region is a quadrilateral.

The feasible region of the $L$.$P$.$P$. (Linear Programming Problem) to maximize $z = 70x + 50y$ subject to the constraints $8x + 5y \leq 60$,$4x + 5y \leq 40$ and $x \geq 0, y \geq 0$ is:

Similar Questions

The objective function $z = 4x + 5y$ subject to the constraints $2x + y \geq 7$,$2x + 3y \leq 15$,$y \leq 3$,$x \geq 0$,and $y \geq 0$ has a minimum value at which point?

If the feasible region is as shown in the figure,then the related inequalities are:

The shaded area in the given figure is a solution set for some system of inequations. The maximum value of the function $z=10x+25y$ subject to the linear constraints given by the system is

The maximum value of $z = 3x + 5y$ subject to the constraints $3x + 2y \leq 18$,$x \leq 4$,$y \leq 6$,$x, y \geq 0$,is

The shaded area in the figure below is the solution set for a certain linear programming problem. The linear constraints are given by:

Vedclass Test Series

Exam Paper Generator

Online Exam Module