Respuesta :
Answer:
cheapest cost = $125.58
Explanation:
Given data:
w = w L = 2w h = h
Volume: V = L×w×h
10 = (2w)(w)(h)
10 = 2hw^2 solving for h we have
[tex]h = \frac{5}{w^2}[/tex]
Cost: [tex]C(w) = 10(Lw) + 2[4(hw)] + 2[4(hL)])[/tex]
[tex]= 10(2w^2) + 2(4(hw)) + 2(4(h)(2w))[/tex]
[tex]= 20w^2 + 2[4w(5/w^2)] + 2[8w(5/w^2)][/tex]
[tex] = 20w^2 + 20/w + 80/w[/tex]
[tex] = 20 w^2 + 100w^{-1}[/tex]
[tex]C'(w) = 40w - 100w^{-2}[/tex]
Critical numbers:
(40w^3 - 100)/w^2 = 0 multiply and divide by w^2
40w^3 -100 = 0
40w^3 = 100
w^3 = 2.5
w = 1.35 m
L = 2.71 m
h = 2.74 m
Cost: C = 10(Lw) + 2[4(hw)] + 2[4(hL)])
= 10(2.71)(1.35) + 2[4(2.74)(1.35)] + 2[4(2.74)(2.71)])
= $125.58 cheapest cost
