Algebra

posted by .

A rectangular box with the volume 320 cu ft is built with a square base and a square top. The cost is $1.50/sg ft for the bottom, $2.50/sq ft for the sides and $1.00/sq ft for the top. Let x=the lenth of the base in feet. Express the cost of the box as a function of x. Where do I start?

You can see this better if you draw a rectangular box. The base is x and x so the area will be x^2.
The volume of the box is x^2 x height = x^2*h = 320 so solving for h we have
h=320/x^2.

Now figures the cost.
For the bottom the area is x^2.
The cost is 1.50/ft^2*(x^2) = ??

The cost of the top is
2.50/ft&2 *(x^2) = ??

The area of the sides is
h*x = (320/x^2)*x and the cost is that times 2.50/ft^2 and that times 2 (since there are two sides. Remember to put this cost in terms of x.

Then add all the costs.

Post your work if you get stuck.

Thx! I was making this harder than it needed to be! I originally got started like you said and thought it looked too easy!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    A rectangular box with a square base and top is to be made to contain 1250 cubic feet. The material for the base costs 35 cents per square foot, for the top 15 cents per square foot, and for the sides 20 cents per square foot. Find …
  2. Calculus - dimensions of a box?

    A rectangular box with a square bottom and a volume of 256 cubic feet is to be constructed. The top and bottom cost $ .10 per square foot to make and the four sides cost $ .05 per square foot to make. Find the approximate dimensions …
  3. Calc

    A closed box with a square base is to be constructed so that its volume is 324 cubed feet. The material for the top and bottom cost is $3 per square foot, and that for the sides $2 per square foot. Find the dimensions of the box so …
  4. Math

    Ignoring the walls’ thickness, determine the outside dimensions that will minimize a closed box’s cost if it has a square base and top, if its volume is 32 cubic meters, and if the cost per square meter for the top, bottom, and …
  5. Math

    Ignoring the walls’ thickness, determine the outside dimensions that will minimize a closed box’s cost if it has a square base and top, if its volume is 32 cubic meters, and if the cost per square meter for the top, bottom, and …
  6. math

    A rectangular box with a volume of 320 cubic units is to be constructed with a square base and top. The cost per square foot of the bottom is 15 cents, for the top 10 cents, and for the sides is 2.5 cents. Find the dimensions that …
  7. Math

    A rectangular box with a square base of length x and height h is to have a volume of 20ft^3. The cost of the top and bottom of the box is 20 cents per square foot and the cost of the sides is 8 cents per square foot. Express the cost …
  8. Math

    You were assigned to construct qn open-top box with a square base from two materials, one for the bottom and one for the sides. The volume of a box is 78 cubic inches. The cost of the material for the bottom is Php 4 per square inch, …
  9. Math

    You were assigned to construct qn open-top box with a square base from two materials, one for the bottom and one for the sides. The volume of a box is 78 cubic inches. The cost of the material for the bottom is Php 4 per square inch, …
  10. calculus

    Melissa wants to make a rectangular box with a square base and cover its top and bottom faces with velvet, which will cost her $3 per square inch, and the sides with silk, which will cost her $5 per square inch. The box should have …

More Similar Questions