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Ierofanga [76]
3 years ago
15

A manufacturer wants to construct a box whose base length is 4 times the base width. The material to build the top and bottom co

st 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.
Mathematics
1 answer:
Nitella [24]3 years ago
6 0

Answer:

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

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Answer:

fraction of the games did the team win is = \frac{3}{4}

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Step-by-step explanation:

given data

baseball team played = 32 games

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to find out

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solution

we know total game = 32 and lost 8

so win is total - lost = 32 - 8 = 24

so

fraction of the games did the team win is = \frac{\frac{24}{8} }{\frac{32}{8} }  

fraction of the games did the team win is = \frac{3}{4}

and

so total game 24 winning is  \frac{5}{8}

so katy winning is  24*\frac{5}{8}

katy winning = 3 × 5 = 15

and

losing  \frac{1}{4}

total lose game 8

so Katy  lose = 8 ×  \frac{1}{4} = 2

so

Katy play game = 15 + 2 = 17

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