calculus
posted by john .
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 per square meter for the sides.
a) Write a function C, the cost of constructing the described tank as a function of l(the length) and h(the height).
b) Write a function C, the cost of constructing the described tank as a function of a single variable.
c) What is the cost of the least expensive tank? (show all work)

let its length be l m
and its height by h m
volume = 4lh
but 4lh = 36
h = 9/l
a) cost = 10(4l) + 5(2lh) + 5(8h)
= 40l + 10lh + 40h
b) cost = 10(4l) + 5(2l)(9/l) + 40(9/l
= 40l + 90 + 360/l ,where l ≠ 0
c) d(cost)/dl = 40 + 0  360/l^2 = 0 for a min of cost
40 = 360/l^2
l^2 = 9
l = √9 = 3
when l = 3, h = 9/3 = 3
dimensions for min cost = 3by4 for the base and a height of 3
cost = 330.00
test: take a value slightly higher and lower than l = 3
l = 3.1, cost = 330.13 , higher
l = 2.9 , cost = 330.14 , higher
answer looks good
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? 
AP CALCULUS!!! HELPP
related rates: the base of a pyramidshaped tank is a square with sides of length 12 meters, and the vertex pyramid is 13 meters above the base. the tank is filled to a depth of 5 meters, and water is flowing into the tank at the rate … 
AP CALCULUS!! HELPPP URGENT
related rates: the base of a pyramidshaped tank is a square with sides of length 12 meters, and the vertex pyramid is 13 meters above the base. the tank is filled to a depth of 5 meters, and water is flowing into the tank at the rate … 
Calculus AB/AP
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 … 
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 holding pen for fish is to be made in the form of a rectangular solid with a square base and open top. The base will be slate that costs $4 per square foot and the sides will be glass that costs $5 per square foot. If the volume … 
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 … 
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 …