Question

WILL GIVE MEDAL FOR RIGHT ANSWER:
A rectangular storage container with an open top is to have a volume of 26 cubic meters. The length of its base is twice the width. Material for the base costs 12 dollars per square meter. Material for the sides costs 9 dollars per square meter. Find the cost of materials for the cheapest such container.

Answer 1

i see
L=2W
B=2W*W

Answer 2

V=2W^2 * H

Answer 3

26=2W^2 * H
Cost = 54HW+24W^2

Answer 4

Cost = 702/w + 24w^2

Answer 5

derivative = 0

Answer 6

\[702w^{-1}+24w^2\]
derivative =
\[-702w^{-2}+48w\]

Answer 7

\[-\frac{ 702 }{ w^{2} }+48w=0\]\[48w=\frac{ 702 }{ w^{2} }\]\[w=\sqrt[3]{\frac{ 117 }{ 8 }}\]

Answer 8

\[w \approx 2.4454866232544\]

Answer 9

the least amount of cost is when
L = 4.8909732465088
W= 2.4454866232544
H =2.1737658873373