The top and bottom margins of a poster are 6 cm each, and the side margins are 4 cm each. if the area of the printed material on the poster is fixed at 384 square centimeters, the dimensions of the poster of the smallest area would be

The dimensions of the poster of the smallest area would be 24×36 cm.

Step-by-step explanation:

Let x and y be the width and height respectively of the printed area, which has fixed area.

If the area of the printed material on the poster is fixed at 384 square centimeters.

i.e.

The top and bottom margins of a poster are 6 cm each is y+1.

The total width of the poster including 4 cm at sides is x+8.

The area of the total poster is

Substitute the value of y,

Derivate w.r.t x,

Put A'=0,

Derivate again w.r.t x,

is positive for x>0,

A is concave up and x=16 is a minimum.

The corresponding y value is

The total poster width is x+8=16+8=24 cm

The total poster height is y+12=24+12=36 cm

Therefore, the dimensions of the poster of the smallest area would be 24×36 cm.