Question

I need help in Calculus one (optimization)
The top and bottom margins of a poster are 2 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 388 square centimeters, find the dimensions of the poster with the smallest area. Refer to the given diagram. Let \,w be the width (in centimeters) of the poster and let \,h be the height (in centimeters) of the poster. Walk me through it please, not just an answer

Answer 1

This is the image the question is referring to

Answer 2

I just learned this like.. last week :P
lemme see if I can try, gimme a sec @Young-Lau

Answer 3

@jigglypuff314 Aight, thanks.

Answer 4

step 1. identify all the information they gave you

height must be at least 4 cm
width must be at least 16 cm
A = 388 cm^2
then the formulas A = h*w
and P = 2w + 2h

got that?

Answer 5

yes

Answer 6

then from the two area formulas
A = 388 and A = h*w
388 = h*w

purpose is to get only to variables in the Perimeter formula
so get a h or a w in terms of the other
I did h = 388/w

follow?

Answer 7

yes

Answer 8

then plus what we just got into the P = 2w + 2h
P = 2w + 2(388)/w
P = 2w + 776*w^(-1)

then take the derivative of P in terms of w
so dP/dw = ?

Answer 9

p'=2-776/w^2

Answer 10

yes :)
when what would be the zero for that?
aka "critical point"
aka "minimum"

Answer 11

+ or - sqrt(776/2)
but negative doesnt make sense so
sqrt(776/2)

Answer 12

yes! :)

that should be right...
usually there's like a "justify" at the end of the question
do you have to do that?
like prove that what you got was a minimum and not a max?

Answer 13

No. Thanks for the help. Really appreciate it.
Also, Jigglypuff is my favorite pokemon.

Answer 14

xD Glad I could help :)