Find a formula for the volume of the parcel in terms of and . 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 and ? Equation:
Solve this equation for in terms of .
Find a formula for the volume in terms of . cubic inches
What is the domain of the function ? Note that must be positive and ; consider how these facts, and the constraint that girth plus length is 108 inches, limit the possible values for . 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 Optimal dimensions: and inches
You can earn partial credit on this problem.