ok, looks like you are saying that you have a box with a square base of r inches each and a height of x inches
volume = r^2 x = 78
so x = 78/r^2
cost = 4(area of base) + 3(4 sides)
= 4r^2 + 12 rx
= 4r^2 + 12(78/r^2)(r) = 4r^2 + 936/r
b) makes no sense to me, since the volume is to be 78 inches^3, your given case does not give me that volume.
c)
d(cost)/dr = 8r - 936/r^2
= 0 for a max/min
936/r^2 = 8r
r^3 = 117
r = appr 4.891
x = appr 3.261
min cost = 4(4.891) + 936/4.891
= appr 210.936.. <------ minimum cost
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, while the cost of the material
for
the sides is Php 3 per square inch.
(a) Determine a function C for the cost of constructing the box as function of the side r, of the base.
(b) What is the cost of constructing the box rt x is 2 inches? 3.5 inches?
(c) What should be the dimension of the box that will give the minimum cost of constructing it?
Justify
your answer.
1 answer
0 answers