Aimee is shipping a care package to her friend in college, and she has a piece of
cardboard with which to create a box. A rectangular cardboard sheet measuring 20
inches by 40 inches is to be used by cutting out square corners of measurex inches.
40 inches
XI
X
L.
20 inches
I

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okpalawalter8 okpalawalter8 · Answer 1 · 2022-07-13T20:12:28+02:00

Aimee is shipping a care package to her friend in college, the max volume of the box is mathematically given as

V=1539.6007

Generally, the equation for the height is mathematically given as

V=(20-2x)(40-2x)x

Where x is the height

V=4x^3-120x^2+800x

differentiate v and solve

dv/dx=3x^2-60+200

3x^2-60+200=0

Therefore

x=[tex]\frac{60\pm \sqrt{60^2-4x3x200}}{2*3}[/tex]

x=[tex]\frac{60-34.64}{6}[/tex]

x=4.2265

In conclusion, the second differentiation of v and solve we have

d^2v/dx^2=24-240

Hence

d^2v/dx^2< 0

V=(20-2x(40-2x)x

subsitute x

V=(20-2(4.2265))(40-2(4.2265))(4.2265)

V=1539.6007