calculus

posted by .

Find the minimum cost of producing a can that contains 1000mm^3 if the cost of the metals is 2 cents per mm^2 and the cost to weld the seams is 1 cent per mm. Assume three welds;one around the top, one around the bottom, and one down the side.

  • calculus -

    let the radius of the can be r mm
    and its height be h mm

    area = 1 rectangle + 2 circles
    = 2pi(r)(h) + 2pi(r^2)


    seems length = 2 circuferences + height of can
    = 2(2pi(r)) + h
    = 4pi(r) + h

    so Cost = 2[2pi(r)(h) + 2pi(r^2)] + 1[4pi(r) + h]

    but pi(r^2)h = 1000
    so h = 1000/(pi(r^2))

    this should give you a good start, sub h back into the Cost equation,
    find the derivative of Cost,
    then solve for r

    sub back into Cost equation to find minimum cost

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Word Problem Cost minimization

    Don Garcia needs at least 24 units of vitamin A per day. Each green pill provides 4 units and each red pill provides one unit. Green pills cost 3.5¢ each and red pills cost 1¢ each. How many of each kind of pill should he take to …
  2. calculus

    a rectangular box is to have a square base and a volume of 20 ft cubic if the material for the base costs 30 cent per square foot, the material for the sides cost 10 cent per sqaure foot, and the material for the top costs 20 cents …
  3. Math- Linear Programming

    A dog food is to be mixed from three kinds of ingredients: rolled oats, beef parts, and whey. The cost of each is 20 cents, 40 cents, and 35 cents per lb. Each ingredient contains 50, 450, and 200 units of protein and 350, 65, and …
  4. Math

    A can of worms for fishing costs $2.60. There are 20 worms in a can. What is the cost per worm?
  5. Calculus

    *Optimization problem* I'm okay at some optimization problems, but this one has me stumped. You work for a company that manufactures circular cylindrical steel drums that can be used to transport various petroleum products. Your assignment …
  6. Calculus,math

    Constuct a rectangular box with a square base that holds a given volume V0 cm^3.?
  7. math

    The average cost of manufacturing a quantity q of a good, is defined to be a(q) = C(q)/q. The average cost per item to produce q items is given by a(q) = 0.01q2 − 0.6q + 13, for q >0. (a) What is the total cost, C(q),of producing …
  8. math/economics in calculus

    The average cost of manufacturing a quantity q of a good, is defined to be a(q) = C(q)/q. The average cost per item to produce q items is given by a(q) = 0.01q2 − 0.6q + 13, for q >0. I know that the total cost is 0.01q^3-0.6q^2+13q …
  9. Pre Calculus

    A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and …
  10. MATH

    I am new to this site. I am not sure if my last post went thru, with my calculations for review, so I will copy and paste my entire query. Thanks for your assistance. === Additional questions: this is for a form I need to fill out …

More Similar Questions