Answer:
y = -20x + 100
Step-by-step explanation:
As per your requirement For Part B, the solution is
The equation in slope-intercept form to model the relations is below:-
To reach 2 points on the graph the line passes through
lets use p1(0, 100), p2(1, 80)
now we will compute the slope:
= -20
and now use line equation in form point-slope:
y - y1 = m(x - x1)
y - 100 = -20(x - 0)
y = -20x + 100
Answer:
The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.
Step-by-step explanation:
This is a optimization with restrictions problem.
The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).
This restriction can be expressed as:
being x: the side of the square of the cross section and L: length of the package.
The volume, that we want to maximize, is:
If we express L in function of x using the restriction equation, we get:
We replace L in the volume formula and we get
To maximize the volume we derive and equal to 0
We can replace x to calculate L:
The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.