Linear Programming
4 JEE Maths previous year questions on Linear Programming — options free on every question; 1 include the answer & explanation free, the rest unlock with PYQ Pass.
The corner points of the feasible region determined by the following system of linear inequalities \( 2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0 \) are \( (0,0),(5,0),(3,4) \) and \( (0,5) \). Let \( Z=p x+q y \), where \( p, q>0 \). Condition on \( p \) and \( q \), so that the maximum of \( Z \) occurs at both \( (3,4) \) and \( (0,5) \), is
\( q=3 p \)
As the maximum of \( Z \) occurs at both \( (3,4) \) and \( (0,5) \)
\(∴{Z}_{\left(3,4\right)}={Z}_{\left(0,5\right)}\\ \Rightarrow 3p+4q=5q\\ \Rightarrow 3p=q\\ \Rightarrow q=3p\)
The corner points of the feasible region determined by the following system of linear inequalities \( 2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0 \) are \( (0,0),(5,0),(3,4) \) and \( (0,5) \). Let \( Z=p x+q y \), where \( p, q>0 \). Condition on \( p \) and \( q \), so that the maximum of \( Z \) occurs at both \( (3,4) \) and \( (0,5) \), is
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If the number of available constraints is 3 and the number of parameters to be optimised is 4 , then
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If the number of available constraints is 3 and the number of parameters to be optimised is 4 , then
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