Question

The top and bottom margins of a poster are 8 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 390 square centimeters, find the dimensions of the poster with the smallest area.

Answer 1

for the width i got 21.96424004 but for some reason i keep getting the height wrong

Answer 2

equation for Area: (x)(y)= 390
Separate for y: y= 390/x
New area equation with border (x+ 8)(y+16)
Multiply it out: (xy + 16x+8y+128

Now plug value for A initial in for xy , which is 390
390+ 16x +8y+128

Plug in y
390+16x+8(390/x)+128 = A

Differentiate to optimize you'd get, then set to 0 to find relative minimum value
16-8(390/x^2)=0
x^2= 8*390 /16
x= 13.96
y=390/x = 390/13.96=27.928=27.93

Answer 3

ok so the height is 21.9642004 and height = 27.93

Answer 4

thank you!!