Question

A delivery package in rectangular shape should have a maximum combined length and girth (perimeter of a cross section) of 150 inches. Which of the following functions would best describe the volume of the package where a and b are elements of real numbers and are less than or equal to 150 ?

Answer 1

The volume function for the rectangular package with a maximum combined length and girth of 150 inches can be expressed as ((150 - 2b) / (b + 2)) * b * h.

Step-by-step explanation:

The volume of a rectangular package can be calculated by multiplying its length, width, and height. Since the package has a maximum combined length and girth of 150 inches, we can write the equation:

2a + 2b + a*b = 150

To find the volume function, we need to express one variable in terms of the other. Let's solve the equation for 'a' in terms of 'b':

1. Rearrange the equation: a*b + 2a + 2b = 150
2. Factor out 'a' on the left side: a*(b + 2) = 150 - 2b
3. Divide both sides by (b + 2): a = (150 - 2b) / (b + 2)

Now, we can substitute this expression for 'a' in the volume equation:

Volume = a*b*h = ((150 - 2b) / (b + 2)) * b * h