Find a formula for the volume of the parcel in terms of x and y. Volume = cubic inches The problem statement tells us that the parcel's girth plus length may not exceed 108 inches. In order to maximize volume, we assume that we will actually need the girth plus length to equal 108 inches. What equation does this produce involving x and y? Equation: Solve this equation for y in terms of x. y = Find a formula for the volume V(x) in terms of x. V(x) = cubic inches What is the domain of the function V? Note that x must be positive and y > x; consider how these facts, and the constraint that girth plus length is 108 inches, limit the possible values for x. Give your answer using interval notation. Domain: Find the absolute maximum of the volume of the parcel on the domain you established above and hence also determine the dimensions of the box of greatest volume. Maximum Volume = cubic inches %3D Optimal dimensions: x = and y = inches

Find a formula for the volume of the parcel in terms of x and y. Volume = cubic inches The problem statement tells us that the parcel's girth plus length may not exceed 108 inches. In order to maximize volume, we assume that we will actually need the girth plus length to equal 108 inches. What equation does this produce involving x and y? Equation: Solve this equation for y in terms of x. y = Find a formula for the volume V(x) in terms of x. V(x) = cubic inches What is the domain of the function V? Note that x must be positive and y > x; consider how these facts, and the constraint that girth plus length is 108 inches, limit the possible values for x. Give your answer using interval notation. Domain: Find the absolute maximum of the volume of the parcel on the domain you established above and hence also determine the dimensions of the box of greatest volume. Maximum Volume = cubic inches %3D Optimal dimensions: x = and y = inches

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....

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