The objective function of a Linear Programmin | vedclass

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(D) According to the Fundamental Theorem of Linear Programming,if an optimal solution exists for a linear programming problem,it must occur at one of

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at least one of the corner points.

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(D) 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. If the objective function attains the same optimal value at two corner points,then every point on the line segment joining these two points is also an optimal solution. Therefore,the objective function always attains its optimum value at at least one of the corner points.

Column	Value
$A$. Maximum of $z$	$300$
$B$. Constant value	$325$

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

Similar Questions

Solve the following Linear Programming Problem graphically:
Minimise $Z = x + 2y$
subject to the constraints:
$2x + y \geq 3$
$x + 2y \geq 6$
$x, y \geq 0$

The corner points of the feasible region determined by the system of linear constraints are $(0,0), (0,40), (20,40), (60,20), (60,0)$. The objective function is $z=4x+3y$. Compare the quantity in Column $A$ and Column $B$.

Column Value

$A$. Maximum of $z$ $300$

$B$. Constant value $325$

The corner points of the feasible region are $(0,10), (5,5), (15,15), (0,20)$. The maximum value of $Z = 3x + 9y$ is . . . . . . .

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:

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