(D) For the maximum value of $z$ to occur at both points $(15, 15)$ and $(0, 20)$, the value of $z$ must be equal at these two points.Substitute the c

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(D) For the maximum value of $z$ to occur at both points $(15, 15)$ and $(0, 20)$, the value of $z$ must be equal at these two points.Substitute the coordinates into the objective function $z = px + qy$:At $(15, 15)$, $z_1 = p(15) + q(15) = 15p + 15q$.At $(0, 20)$, $z_2 = p(0) + q(20) = 20q$.Equating $z_1$ and $z_2$:$15p + 15q = 20q$.Subtract $15q$ from both sides:$15p = 5q$.Divide by $5$:$q = 3p$.

Class 12 Mathematics Linear Programming MCQ based Question

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

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A
$p = q$
B
$p = 2q$
C
$q = 2p$
D
$q = 3p$

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MediumGUJCET 2026

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

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Consider a $LPP$ given by minimize $Z = 6x + 10y$. Subject to $x \geq 6, y \geq 2, 2x + y \geq 10, x \geq 0, y \geq 0$. Redundant constraints in this $LPP$ are $....$

The $LPP$ to maximize $z = 2x + 5y$ subject to the constraints $x + 3y \leq 6$, $2x + 6y \leq 18$, $x \geq 0$, $y \geq 0$ has:

Show that the minimum of $Z$ occurs at more than two points.Minimise and Maximise $Z = x + 2y$subject to $x + 2y \geq 100, 2x - y \leq 0, 2x + y \leq 200; x, y \geq 0$.

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?

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Show that the minimum of $Z$ occurs at more than two points.
Minimise and Maximise $Z = x + 2y$
subject to $x + 2y \geq 100, 2x - y \leq 0, 2x + y \leq 200; x, y \geq 0$.