calculus

posted by .

a rectangular box with a square bottom is to have a volume of 1000 cubic inches. the bottom cost $100 per cubic inch, the sides are $25 per square inch and there is no top. what are the dimensions of the box that has materials costing the least

  • calculus -

    I bet the bottom is 100/in^2, not cubic.

    size of box: s^2 * h s is side dimention on bottom.

    cost= 100*s^2+ 4*25sh

    but h= 1000/s^2

    cost= 100s^2+100s(1000/s^2)

    dcost/ds= 200s-100*1000/s^2=0

    200s^3=100,000
    s= cuberoot(500)=7.94in
    h= 1000/7.94^2=15.9in

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  2. calculus

    a closed box with square base is to have a V= 2000in^3. The material for the top and bottom of the box is to cost $3 per square inch and the material for the sides is the cost $1.50 per square inch. If the cost of the material is to …
  3. 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 …
  4. pre-calculus

    A company plans to manufacture a container having the shape of a right circular cylinder, open at the top, and having a capacity of 24pi cubic inches. If the cost of the material for the bottom is $.30 per square inch and that for …
  5. Calculus

    A box with square base and rectangular sides is being designed. The material for the sides costs 20 cents per square inch and that for the too and bottom costs 10 cents per square inch. The box is to hold 150 cubic inches. What dimension …
  6. 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, …
  7. 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, …
  8. 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 …
  9. math

    A closed cylindrical storage container with a volume of 2800 cubic inches. The material for the top and bottom will cost $3 per square inch and the material for the sides will cost $4 per square inch. A) What dimensions of the container …
  10. Calculus

    A rectangular box with a square base and cover is to have a volume of 2500 cubic feet. If the cost per square foot for the bottom is $2, for the top is $3, and for the sides is $1, what should the dimensions be in order to minimize …

More Similar Questions