SOLUTION: Cost of material. A rectangular box with volume 320ft^3 is built with a square base and top. The cost is $1.50/ft^2 for the bottom, $2.50/ft^2 for the sides, and $1/ft^2 for the to

Question 39285This question is from textbook College Algebra
: Cost of material. A rectangular box with volume 320ft^3 is built with a square base and top. The cost is $1.50/ft^2 for the bottom, $2.50/ft^2 for the sides, and $1/ft^2 for the top. Let x=the length of the base, in feet.
a) Express the cost of the box as a function of x.
b) Find the domain of the function. This question is from textbook College Algebra

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Cost of material. A rectangular box with volume 320ft^3 is built with a square base and top. The cost is $1.50/ft^2 for the bottom, $2.50/ft^2 for the sides, and $1/ft^2 for the top. Let x=the length of the base, in feet.
a) Express the cost of the box as a function of x.
Cost = cost of bottom + cost of top +4(cost of one side)
cost of bottom= $1.5x^2
cost of top =$1(x^2)
To get cost of side need to know the height of a side, as follows.
V=lwh
320=x^2h
h=320/x^2
Area of one side is base(height)=x(320/x^2)=320/x
Cost of 4 sides is 4($2.5)(320/x)=3200/x
EQUATION:
Cost =1.5x^2+x^2+3200/x
= 2.5x^2+3200/x
b) Find the domain of the function.
Domain of the FUNCTION is all Real numbers except x=0
Domain of the function as a model of the problem is
x>0
Cheers,
Stan H.

RELATED QUESTIONS
70) Cost of Material. A rectangular box with volume 320ft cubed is built with a square... (answered by THANApHD)

A closed rectangular box is to be constructed with a square base. The material for the... (answered by josgarithmetic)

A box, with rectangular sides, base and top is to have a volume of 2 cubic feet. It has a (answered by josmiceli)

A rectangular box is to have a square base and a volume of 30 ft^3. The material for the... (answered by josgarithmetic)

A closed rectangular container with a square base is to have a volume of 18000 inches^3 . (answered by ikleyn)

Hi. I don't know how to set up this problem, let alone solve it. Thanks in advance. A... (answered by josgarithmetic)

A rectangular box is to have a square base and a volume of 20 feet cubed. If the... (answered by ankor@dixie-net.com,josmiceli)

A rectangular box is to have a square base and a volume of 36 feet cubed. If the material (answered by greenestamps)

This is a derivative minimum word problem. It says first find the function f(x)that we... (answered by KMST)