The objective function of a Linear Programmin | vedclass

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

Question

(C) Let $Z = ax + by$ be the objective function. According to the Fundamental Theorem of Linear Programming,if an optimal solution exists for a linear

Vedclass · Accepted Answer

At least one of the corner points

Vedclass · Answer

(C) Let $Z = ax + by$ be the objective function. According to the Fundamental Theorem of Linear Programming,if an optimal solution exists for a linear programming problem,it must occur at one of the corner points (vertices) of the feasible region. Even if the optimal value is attained at more than one point,it is guaranteed to be attained at at least one of the corner points of the convex polygon formed by the constraints. Therefore,the objective function attains its optimum value at at least one of the corner points.

The objective function of a Linear Programming Problem $(LPP)$ defined over a convex set attains its optimum value at:

Similar Questions

The constraints $-x_{1} + x_{2} \leq 1$,$-x_{1} + 3x_{2} \leq 9$,and $x_{1}, x_{2} \geq 0$ define:

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 corner points of the feasible region are $A(0,0)$,$B(16,0)$,$C(8,16)$,and $D(0,24)$. The minimum value of the objective function $z = 300x + 190y$ is . . . . . . .

For the linear programming constraints $x+2y \geq 10$,$3x+4y \leq 24$,$x \geq 0$,and $y \geq 0$,which of the following is not a corner point of the feasible region?

The following graph represents a feasible region. The minimum value of $z = 5x + 4y$ is $\ldots \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module