A manufacturer wants to construct a box whose base length is 4 times the base width. The material to build the top and bottom cost 8 dollars per ft.2 and sides 5 dollars per ft.2. If the box must have a volume of 72 ft.3, determine the dimensions that will minimize cost.

width = 1.77845 ft

length = 7.1138 ft

height = 5.691 ft

total cost = $759.09

Step-by-step explanation:

volume = length x width x height

length = 4 width

base of the rectangle = 4 x 1 w = 4w²

72 (volume) = 4w²h

18 = w²h

f(c) = (2 x 4w² x $10) + (2 x wh x $5) + (2 x 4wh x $5)

f(c) = 80w² + 10wh + 40wh

f(c) = 80w² + 50wh

since we need only 1 variable (width), we have to substitute h:

h = 18/w²

f(c) = 80w² + 50w(18/w²) = 80w² + 900/w

f'(c) = 160w + 900/w²

0 = (160w³ + 900)/w²

0 = 160w³ + 900

0 = 20(8w³ + 45)

0 = 8w³ + 45

8w³ = -45

w³ = -45/8

w = ∛-45/8 = -1.77845 and 1.77845

since w cannot be negative, then it must be 1.77845

it can be to see completed examples before writing, in order to examine what makes for an effective piece. see how these intros give some context before posing the topic and lead naturally into the body paragraphs, where the evidence will be listed. you can imagine how the author has organized the rest of the piece.

"we buried my cousin last summer. he was 32 when he hanged himself from a closet coat rack in the throes of alcoholism, the fourth of my blood relatives to die prematurely from this deadly disease. if america issued drinking licenses, those four men—including my father, who died at 54 of liver failure—might be alive today. that is a good example piece   some steps that are .

. writing something that happened to you

.read a book you like to get ideas from there

. lastly you can make a venn diagram

hope this plz make brainliest

step-by-step explanation: