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Model Paper 5 — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSModel Paper 51 Mark
Question
A Linear Programming Problem is as follows:
Maximize/Minimize objective function $Z = 2x - y +5$
Subject to the constraints
$3 x+4 y \leq 60$
$x+3 y \leq 30$
$x \leq 0, y \geq 0$
In the corner points of the feasible region are $A(0, 10), B(12, 6), C(20, 0)$ and $O(0,0),$ then which of the following is true?
✓

Answer

$(a)$ Minimum value of $Z$ is $-5$
Corner Points Value of $Z = 2x - y + 5$
$A(0, 10)$ $Z=2(0)-10+5 = -5\ ($Minimum$)$
$B(12, 6)$ $Z2(12)-6+ 5 = 23$
$C(20, 0)$ $Z=2(20)-0+5 = 45\  ($Maximum$)$
$O(0,0)$ $Z=0(0)-0+5=5$
So the minimum value of $Z$ is $-5.$

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