Ask Question

The volume of the box must be 100 cubic meters. the cost of the material to be used on the sides is $11 per square meter and the cost of the material to be used on the bottom is $19 per square meter. what is the minimum cost?

+5
Answers (1)
  1. 7 April, 03:44
    0
    V = Lwh

    10 = (2w) (w) (h)

    10 = 2hw^2

    h = 5/w^2

    Cost: C (w) = 10 (Lw) + 2[6 (hw) ] + 2[6 (hL) ])

    = 10 (2w^2) + 2 (6 (hw)) + 2 (6 (h) (2w)

    = 20w^2 + 2[6w (5/w^2) ] + 2[12w (5/w^2) ]

    = 20w^2 + 60/w + 120/w

    = 20 w^2 + 180w^ (-1)

    C' (w) = 40w - 180w^ (-2)

    Critical numbers:

    (40w^3 - 180) / w^2 = 0

    40w^3 - 180 = 0

    40w^3 = 180

    w^3 = 9/2

    w = 1.65 m

    L = 3.30 m

    h = 1.84 m

    Cost: C = 10 (Lw) + 2[6 (hw) ] + 2[6 (hL) ])

    = 10 (3.30) (1.65) + 2[6 (1.84) (1.65) ] + 2[6 (1.84) (3.30) ])

    = $165.75 cheapest cost
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “The volume of the box must be 100 cubic meters. the cost of the material to be used on the sides is $11 per square meter and the cost of ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers