L = 2 w
V = L w h = 2 w^2 h = 10
so w^2 h = 5
base area = L w =2 w^2
base cost = 18 w^2
ends area = 2 w h
ends cost = 300 w h
sides area = 2 L h = 4 w h
sides cost = 600 w h
total cost = 900 w h + 18 w^2
but h = 5/w^2
c = 900 w (5/w^2) + 18 w^2
c = 4500/w + 18 w^2
dc/dw = -4500/w^2 + 36 w
= 0 for min
36 w^3 = 4500
w = 5 sure enough
A rectangular storage container with an open top is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $9 per m2. Material for the sides costs $150 per m2. Find the dimensions of the container which will minimize cost and the minimum cost. I need the minimum cost , I found the dimensions to length=10
Width=5 height=0.2. Thanks so much in advance!
4 answers
$4500 comes up as incorrect :(
Where did you get 4500 from ?
Damon correctly found w = 5
and his cost equation was
c = 4500/w + 18 w^2
= 4500/5 + 18(25) = 1350
Damon correctly found w = 5
and his cost equation was
c = 4500/w + 18 w^2
= 4500/5 + 18(25) = 1350
So sorry for that!!
1 answer