Calculus AB/AP
posted by Julie .
A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4 meters and its volume is 36 cubic meters. If building the tank costs $8 per square meter for the base and $4 per square meter for the sides, what is the cost of the least expensive tank?

Calculus AB/AP 
Steve
If we let the length be L and the height be H, then we have
4LH = 36
LH = 9
L = 9/H
The cost
C = 4L*8 + 4*4H*4
C = 32(9/H) + 64H
C = 288/H + 64H
dC/dH = 64  288/H^2
dC/dH = 0 when H = √2.5 = 2.12
so L = 4.24
C = 288/2.12 + 64*2.12 = $271.53
Respond to this Question
Similar Questions

math
A box with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 8 meters and its volume is 72 cubic meters. If building this box costs $20 per square meter for the base and … 
MATH!!
A fish tank with a rectangular base has a volume of 3,360 cubic inches. The length and width of the tank are 14 inches and 12 inches, respectivily. Find the height, in inches, of the tank? 
Algebra
An open box is to be constructed from a rectangular sheet of tin 3 meters wide by cutting out a 1meter square from each corner and folding up the sides. The volume of the box is to be 2 cubic meters. What is the length of the tin … 
calculus
A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4 meters and its volume is 36 cubic meters. Building the tank costs $10 per square meter for the base and $5 … 
Calc 1 (Optomization)
A rectangular storage container with an open top is to have a volume of k cubic meters. The length of its base is twice its width. The material for the base costs $6 per square meters and the material for the sides costs $10 per square … 
Math
An open rectangular tank (no top) with volume 11 cubic meters has a square base. The base has side x m. Write an equation for the surface area of the tank as a function of the length x. Surface Area = ? 
Calculus
A rectangular storage container with an open top is to have a volume of k cubic meters. The length of its base is twice its width. The material for the base costs $6 per square meters and the material for the sides costs $10 per square … 
algebra
An open box is to be constructed from a rectangular sheet of tin 5 meters wide by cutting 1 square meter from each corner and folding up the sides. The volume of the box is to be 18 cubic meters. What is the length of the tin rectangle? 
Calculus
A rectangular tank with a square base, an open top, and a volume of 4,000 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. I'm not understanding how to get started … 
Calculus
A box has rectangular sides, top and bottom. The volume of the box is 3 cubic meters. The height of the box is half the width of the base. Express the total surface area of the box in terms of the height of the box.