Rectangular Package

[nycmathguy]

Section 2.5
Question 104

For this problem, I seek the set up for all three parts.

 

[MathLover1]

a.

volume
V=length*width*height
length=width=x
height=y
so
V=x*x*y
V=x^2*y

given

perimeter of base+height is 120
4x+y=120
y=120-4x


then
V=x^2(120-4x)
V=120x^2-4x^3
V=-4x^3+120x^2


b

max at (20,16000)

c.
13500=-4x^3+120x^2

x = 15

 

[nycmathguy]

a.

volume
V=length*width*height
length=width=x
height=y
so
V=x*x*y
V=x^2*y

given

perimeter of base+height is 120
4x+y=120
y=120-4x


then
V=x^2(120-4x)
V=120x^2-4x^3
V=-4x^3+120x^2


b
View attachment 480

max at (20,16000)

c.
13500=-4x^3+120x^2

x = 15

Nicely-done. I requested the set up only for each part but thank you for working it out.

What about the two unanswered threads below?

1. Verifying Upper & Lower Bounds
   
   
2. Descartes' Rule of Signs

They are two separate threads in this forum. We then move on to Section 2.6 aka Rational Functions.