(D) To find the minimum value of the objective function $Z = 4x + 6y$,we evaluate $Z$ at each corner point:$1$. At $(0,2): Z = 4(0) + 6(2) = 12$$2$. A

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Any point on the line segment joining the points $(0,2)$ and $(3,0)$

(D) To find the minimum value of the objective function $Z = 4x + 6y$,we evaluate $Z$ at each corner point:$1$. At $(0,2): Z = 4(0) + 6(2) = 12$$2$. At $(3,0): Z = 4(3) + 6(0) = 12$$3$. At $(6,0): Z = 4(6) + 6(0) = 24$$4$. At $(6,8): Z = 4(6) + 6(8) = 24 + 48 = 72$$5$. At $(0,5): Z = 4(0) + 6(5) = 30$Since the minimum value of $Z$ is $12$,which occurs at both corner points $(0,2)$ and $(3,0)$,the minimum value of $Z$ occurs at every point on the line segment joining these two points.

Class 12 Mathematics Linear Programming MCQ based Question

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Corner points of the feasible region for an $LPP$ are $(0,2), (3,0), (6,0), (6,8)$ and $(0,5)$. Let $Z = 4x + 6y$ be the objective function. The minimum value of $Z$ occurs at

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Only $(0,2)$
B
Only $(3,0)$
C
The mid-point of the line segment joining the points $(0,2)$ and $(3,0)$
D
Any point on the line segment joining the points $(0,2)$ and $(3,0)$

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Value of the objective function $Z = -50x + 20y$ subject to the constraints $2x - y \geq -5$,$3x + y \geq 3$,$2x - 3y \leq 12$,$x \geq 0$,$y \geq 0$. The corner points of the feasible region are $(0, 5)$,$(0, 3)$,$(1, 0)$,and $(6, 0)$. At which point is the value of $Z$ minimum?

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The corner points of the feasible region determined by the system of linear constraints are $(0,10), (5,5), (15,15), (0,20)$. Let $z = px + qy$,where $p, q > 0$. The condition on $p$ and $q$ so that the maximum of $z$ occurs at both the points $(15,15)$ and $(0,20)$ is $\ldots \ldots$

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Solve the Linear Programming Problem graphically:
Minimise $Z = 3x + 5y$
subject to the constraints:
$x + 3y \geq 3$
$x + y \geq 2$
$x, y \geq 0$

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The following five inequalities form the feasible region: $2x - y \leq 8$,$x + y \leq 20$,$-x + y \geq -10$,$x \geq 0$,$y \geq 0$. Which of the following is a redundant constraint?

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The maximum value of $z = 4x + y$ subject to the constraints $x + y \leq 5$, $2x + y \leq 7$, $3x + 2y \leq 11$, $x \geq 0$, $y \geq 0$ is:

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Corner points of the feasible region for an $LPP$ are $(0,2), (3,0), (6,0), (6,8)$ and $(0,5)$. Let $Z = 4x + 6y$ be the objective function. The minimum value of $Z$ occurs at

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Value of the objective function $Z = -50x + 20y$ subject to the constraints $2x - y \geq -5$,$3x + y \geq 3$,$2x - 3y \leq 12$,$x \geq 0$,$y \geq 0$. The corner points of the feasible region are $(0, 5)$,$(0, 3)$,$(1, 0)$,and $(6, 0)$. At which point is the value of $Z$ minimum?

The corner points of the feasible region determined by the system of linear constraints are $(0,10), (5,5), (15,15), (0,20)$. Let $z = px + qy$,where $p, q > 0$. The condition on $p$ and $q$ so that the maximum of $z$ occurs at both the points $(15,15)$ and $(0,20)$ is $\ldots \ldots$

Solve the Linear Programming Problem graphically:Minimise $Z = 3x + 5y$subject to the constraints:$x + 3y \geq 3$$x + y \geq 2$$x, y \geq 0$

The following five inequalities form the feasible region: $2x - y \leq 8$,$x + y \leq 20$,$-x + y \geq -10$,$x \geq 0$,$y \geq 0$. Which of the following is a redundant constraint?

The maximum value of $z = 4x + y$ subject to the constraints $x + y \leq 5$, $2x + y \leq 7$, $3x + 2y \leq 11$, $x \geq 0$, $y \geq 0$ is:

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Solve the Linear Programming Problem graphically:
Minimise $Z = 3x + 5y$
subject to the constraints:
$x + 3y \geq 3$
$x + y \geq 2$
$x, y \geq 0$