Question

Help with optimization problems..question is attached

Answer 1

let l be the length of the fence parallel to the barn
area = l*w = 200
w=200/l
perimeter = l + (200/l)*2 <-- Minimize
take derivative and solve for 0
1 - 400/l^2 = 0
1 = 400/l^2
l^2 = 400
l = Sqrt[400] = 20
w = 200/20 = 10

Answer 2

so it must be c for teh first one

Answer 3

for the 2nd problem
y=2-x^2 is the height of the rectangle
2x is is the width
maximize 2x(2-x^2)
-2x^3+4x, take derivative and solve for 0
-6x^2+4 = 0
x^2 = 4/6
x=Sqrt[2/3]
area = 2*Sqrt[2/3]*(2-Sqrt[2/3]^2) = 8Sqrt[2/3]/3 which is the same as answer choice b

Answer 4

thanks alot..i hate optimzation problems and i never understnad how to start.

Answer 5

wait how is taht teh same asnwer

Answer 6

8/3 Sqrt[2/3], multiply by 3/3 -> 8/9 *Sqrt(3^2)*Sqrt[2/3] = 8/9 *Sqrt[9*2/3] = 8/9 Sqrt[6]

Answer 7

ohhh i see...sorry its jsut taht wen ppl skip steps sumtimes i get confused

Answer 8

thanks

Answer 9

i didn't actually do that step, just used a calculator to find which answer it matched :p

Answer 10

lol ok thats still smart too =)