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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
In a school, an auditorium was used for its cultural activities.
The shape of the floor of the auditorium is rectangular with dimensions $x$ and $y$ $(x>y)$ and has fixed parameter $p$.
Based on the above information answer the following questions.
The value of $x$, for which area of floor of auditorium is maximum is:
Solution
$p = 2(x+y)$
So
$x+y=\frac{p}{2}$
Hence
$y=\frac{p}{2}-x$
Area of rectangle
$A=xy$
$A=x\left(\frac{p}{2}-x\right)$
$A=\frac{px}{2}-x^2$
To maximize area
$\frac{dA}{dx}=\frac{p}{2}-2x$
Set derivative equal to zero
$\frac{p}{2}-2x=0$
$2x=\frac{p}{2}$
$x=\frac{p}{4}$
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