Question

The top and bottom margins of a poster are 6 ft and the side margins are each 8 ft. If the area of printed material on the poster is fixed at 386 square ft, find the dimensions of the poster with the smallest area.

Answer 1

Answer:

Dimension

Height =29.01

Breadth=38.70

Step-by-step explanation:

Printed area is =386 and margins as specified.

For printed area let height be x and breadth be y.

x*y=386 ⇒ y = $\frac{386}{x}$

Now considering the margins

Height = x+6+6=x+12

Weidth = $\frac{386}{x}$ +8 +8= $\frac{386}{x}$ + 16

Area of poster to be minimised =(x+12)($\frac{386}{x}$ + 16)

Differentiate above area with respect to x and equate to zero to find extrema.

 $\frac{dA}{dx}$ = 16 -$\frac{12*386}{x^{2} }$=0

x=17.01

Now plug value of x in height and breadth

 Height =29.01

Breadth=38.70