A poster is to have an area of 230 in2 with 3 inch margins at the bottom and sides and a 7 inch margin at the top. What dimensions will give the largest printed area?

Question

I need help to find the width and height please

Answer 1

xy = 230

y = 230/x

A(x) = (x-6)(y-10)

= (x-6)(230/x - 10)

= 230 - 10x - 1380/x + 60

= 290 - 10x - 1380/x

0 = dA/dx = -10 + 1380x^(-2)

0 = -10x^2 + 1380

-1380/-10 = x^2

138 = x^2

sqrt(138) = x

which is APPROXIMATELY 11.747340124470730586968506365965

so then y = 230/x = 19.578900207451217644947510609941

Subtract 6 from x and 10 from y to get the max

printable dimensions