SOLUTION: A rectangular box with not top is to contain 2250 cubic inches of volume. Find the dimensions of the box that will minimize the surface area. The length (l) of the base is three

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A rectangular box with not top is to contain 2250 cubic inches of volume. Find the dimensions of the box that will minimize the surface area. The length (l) of the base is three       Log On


   

Question 203505: A rectangular box with not top is to contain 2250 cubic inches of volume. Find the dimensions of the box that will minimize the surface area. The length (l) of the base is three times the width (w)
w= inches
h= inches
l= inches
not sure what I am doing wrong but I am having any luck can someone please thanks
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"length (l) of the base is three times the width (w)" ___ L = 3W

"2250 cubic inches of volume" ___ V = L * W * H ___ 2250 = 3W * W * H ___ 750 / W^2 = H

surface area = (L * W) + 2 (L * H) + 2 (W * H) = 3W^2 + 4500/W + 1500/W = 3W^2 + 6000/W
___ you need to find the minimum of this function

finding the slope of the curve (first derivative) and setting equal to zero -- this is the minimum
___ 0 = 6W - 6000/(W^2) ___ 6000/(W^2) = 6W ___ 1000 = W^3 ___ 10 = W

substituting ___ L = 3(10) = 30 _____ H = 750 / (10^2) = 7.5