Question

Aimee is shipping a care package to her friend in college, and she has a piece of

Answer 1

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

V=1539.6007

What is the max volume of the box?

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=$\frac{60\pm \sqrt{60^2-4x3x200}}{2*3}$

x=$\frac{60-34.64}{6}$

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

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