A poster is to be printed on a rectangular sheet of paper of area 18 ~m ^2 . The margins at the top and bottom of 75 cm each and at the sides 50 cm each are to be left. Then the dimensions i.e. height and breadth of the sheet so that the space available for printing is maximum, are _________ respectively.

Step-by-step solution

Let height and breadth of the sheet be ' y ' m and ' x ' m respectively. array ll & x y=180000 ~cm ^2 & y= 180000 x array The area available for printing is aligned A & =(y-150)(x-100) & = ( 180000 x -150 )(x-100) & =180000- 18000000 x -150 x-15000 & =165000-150 x- 18000000 x aligned array ll & dA ~d x =0-150+ 18000000 x^2 & dA ~d x =0 x^2= 18000000 150 =120000 & x=200 3 ~cm & y= 180000 200 3 =300 3 ~cm array Now, d ^2 ~A ~d x^2 = -36000000 x^3 At x=200 3 ~cm , ~d ^2 ~A ~d x^2 0 Area is maximum at x=200 3 ~cm and y