Postal Regulations Specify That the Combined Length and Girth of a Parcel

Multiple Choice

Postal regulations specify that the combined length and girth of a parcel sent by parcel post may not exceed 108 in. Find the dimensions of the rectangular package that would have the greatest possible volume under these regulations. (Hint: Let the dimensions of the box be by by (see the figure below) . Then, , and the volume . So that . Maximize .)

A) x = 20 inches, y = 37 inches, z = 15 inches, V = 11,100 cubic inches
B) x = 18 inches, y = 18 inches, z = 15 inches, V = 4,860 cubic inches
C) x = 20 inches, y = 36 inches, z = 20 inches, V = 11,664 cubic inches
D) x = 20 inches, y = 36 inches, z = 15 inches, V = 11,100 cubic inches
E) x = 18 inches, y = 36 inches, z = 18 inches, V = 11,664 cubic inches