A poster is to be printed on a rectangular sh | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the height and breadth of the sheet be $y \ m$ and $x \ m$ respectively.Given area of the sheet is $18 \ m^2$,so $x y = 18$.Converting margins

Vedclass · Accepted Answer

$3 \sqrt{3} \ m, 2 \sqrt{3} \ m$

Vedclass · Answer

(B) Let the height and breadth of the sheet be $y \ m$ and $x \ m$ respectively.Given area of the sheet is $18 \ m^2$,so $x y = 18$.Converting margins to meters: top/bottom margins are $0.75 \ m$ each,side margins are $0.5 \ m$ each.The dimensions of the printable area are $(y - 1.5) \ m$ and $(x - 1) \ m$.The area available for printing is $A = (y - 1.5)(x - 1)$.Since $y = \frac{18}{x}$,we have $A = (\frac{18}{x} - 1.5)(x - 1) = 18 - \frac{18}{x} - 1.5x + 1.5 = 19.5 - \frac{18}{x} - 1.5x$.To maximize $A$,differentiate with respect to $x$: $\frac{dA}{dx} = \frac{18}{x^2} - 1.5$.Setting $\frac{dA}{dx} = 0$,we get $\frac{18}{x^2} = 1.5 \Rightarrow x^2 = \frac{18}{1.5} = 12$.Thus,$x = \sqrt{12} = 2 \sqrt{3} \ m$.Then $y = \frac{18}{2 \sqrt{3}} = \frac{9}{\sqrt{3}} = 3 \sqrt{3} \ m$.Checking the second derivative: $\frac{d^2A}{dx^2} = -\frac{36}{x^3}$,which is negative at $x = 2 \sqrt{3}$,confirming a maximum.Therefore,the height is $3 \sqrt{3} \ m$ and the breadth is $2 \sqrt{3} \ m$.

Similar Questions

For a steamer,the consumption of petrol (per hour) varies as the cube of its speed (in $km/hr$). If the speed of the current is steady at $C \, km/hr$,then the most economical speed of the steamer going against the current will be ........... $C$.

Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.

If $x+y=k, x>0, y>0$,then $x^2+y^2$ is minimum,if

Let $k$ and $K$ be the minimum and the maximum values of the function $f(x) = \frac{(1 + x)^{0.6}}{1 + x^{0.6}}$ in $[0, 1]$ respectively,then the ordered pair $(k, K)$ is equal to

$A$ box is to be made with a square base and an open top. If the area of the material used is $48 \, m^2$,then the maximum volume of the box is ........... $m^3$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module