Function of Rectangular Box
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Function of Rectangular Box

[From: ] [author: ] [Date: 11-12-27] [Hit: ]
008, sa=0.so,a)c=(3x^2)(0.008)+(9x/2)(0.003) per square inchc=.......
Math B/6.5

A rectangular packing box, similar to a shoebox without a lid, is three times as long as it is wide, and half as high as it is long. Each square inch of the bottom of the box costs $0.008 to produce, while each square inch of any side costs $0.003 to produce.

(a) Write a function that expresses the cost, c, of the box as a function of its width x.

(b) Using the function written in part (a), determine the dimensions of a box that would cost $0.69 to produce.

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Your facts are: l=3x, l=2h, 3x=2h, ba=0.008, sa=0.003

Your bottom area is: ba=lx and your side area is: sa=lh
so,
a) c=(3x^2)(0.008)+(9x/2)(0.003) per square inch
c=.024x^2+.0135x per square inch

b). 0.69=.024x^2+.0135x

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x=3w h=1.5w
cost of bottom=0.008(3w)(w)
=0.024w²
cost of sides=2(x+w)(h)(0.003)
=2(4w)(1.5w)(0.003)
=0.036w²
a)
total cost=(0.024+0.036)w²
=0.06w²
b)
0.06w²=0.69
w²=0.69/0.06
w²=11.5
w= √11.5
w=3.391 in
h=5.087 in
length=10.173 in

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Um... A shoebox?
1
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