PreCalc
posted by Hannah on .
A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 120 inches.
a. Show that the volume of the package is V(x)= 4xsquared(30x)
b. Use your graphing calculator to find the dimensions of the package that maximize the volume. What is the maximum volume?

The formula V=4xsquared(30x) is correct if the cross section is a square with side equal to x.
I do not have a graphing calculator.
You could find out the maximum volume by calculating with the above formula using various values of x. Try for x between 15 and 25. 
Equation 1: 4x+y=120 > y = 120  4x
Equation 2: x^2(y)=Volume
Combine equations: x^2(1204x) = volume
Distribute: 4x^3 + 120x^2
Those are the initial steps 
A rectangular package to be sent by a delivery service can have a maximum combined length (y) and girth (perimeter of its cross section) of 300 inches. Assume that the width and height are the same (x). Find the equation for the volume of the box in terms of x alone as an expanded polynomial.