(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

KCET 2026 All KCET

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

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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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Maximize the function $Z = 11x + 7y$,subject to the constraints:$x \leq 3, y \leq 2, x \geq 0, y \geq 0$

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Maximize the function $Z = 11x + 7y$,subject to the constraints:
$x \leq 3, y \leq 2, x \geq 0, y \geq 0$

Show that the minimum of $Z$ occurs at more than two points.
Maximize $Z = x + y$,subject to $x - y \leq -1$,$-x + y \leq 0$,$x, y \geq 0$.