f. Use a graphing utility (Desmos is recommended) to graph V. Find the x-value that maximizes the volume of the package, and the associated volume. Round to 2 decimal places. x = V = in y = in³ g. Use your equation in part (d) to find the y-value that is associated with the maximum volume. in
f. Use a graphing utility (Desmos is recommended) to graph V. Find the x-value that maximizes the volume of the package, and the associated volume. Round to 2 decimal places. x = V = in y = in³ g. Use your equation in part (d) to find the y-value that is associated with the maximum volume. in
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
F and g please!
Transcribed Image Text:According to the shipping regulation of a company, the girth plus the length of a parcel sent by mail may
not exceed 61 inches, where by "girth" we mean the perimeter of the smallest end. What is the largest
possible volume of a rectangular parcel with a square end that can be sent by mail? What are the
dimensions of the package of largest volume?
a. Suppose a box has two square ends and other faces are rectangles. Let a represent the length of one
side of the square end and y the length of the longer side. Label the sides.
b. Find a formula for the volume of the box in terms of x and y. V
V
c. The problem statement tells us that the parcel's girth (area of the small end) plus length may not exceed
61 inches. In order to maximize volume, we assume that we will actually need the girth plus length to
equal 61 inches. What equation does this produce involving and y? 4x + y = 61
d. Solve the equation you found in (c) for y. Note that you could solve for æ, but it is easier to solve for y.
y=61-4x
e. Now use your work in (b) and (d) to determine a formula for the volume of the parcel so that this
formula is a function of a single variable (y ). In other words, substitute the expression for y in part (d)
into the equation for V. V = x² (61 − 4x)
x=
f. Use a graphing utility (Desmos is recommended) to graph V. Find the x-value that maximizes the
volume of the package, and the associated volume. Round to 2 decimal places.
y =
2
x y
in
in ³
08
g. Use your equation in part (d) to find the y-value that is associated with the maximum volume.
in
O
OF
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