a sheet of paper for poster is 1 5m2 in area the margins at the top and bottoms - Maths -

Question

a sheet of paper for poster is 1 5m2 in area the margins at the top
and bottoms are to be 6cm and at the side is 4cm wide what should
be dimensions of the sheet to maximise the printed area

Manbar Singh · Accepted Answer

Let the length of the sheet = x cmLet the breadth of the sheet = y
cmNow, area of the sheet = 1 5 m2 = 15000 cm2⇒xy =
15000⇒y = 15000x 1Now, length of the printed portion = x - 12
cmbreadth of the printed portion = y - 8 cmNow, area of printed
portion = x - 12y - 8⇒A = xy - 8x - 12y + 96⇒A = 15000 -
8x - 12 × 15000x + 96⇒A = 15096 - 8x - 180000x⇒dAdx
= -8 + 180000x2For maxima or minima,dAdx = 0⇒-8 + 180000x2 =
0⇒8x2 = 180000⇒x2 = 22500⇒x = 150Now,d2Adx2 =
-360000x3d2Adx2x=150 = -360000150×150×150 =
-875<0So, printed area is maximum at x = 150Now, from 1, y =
15000150 = 100So, length of the sheet = 150 cmbreadth of the sheet
= 100 cm

a sheet of paper for poster is 1.5m2 in area . the margins at the top and bottoms are to be 6cm and at the side is 4cm wide. what should be dimensions of the sheet to maximise the printed area.