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

Postal regulations specify that the combined length and girth of a parcel sent by parcel post may not exceed 120 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 x'' by y'' by z'' (see the figure below) . Then, 2x + 2x + y= 120 , and the volume V=xyz. So that . Maximize f(x,z) .)

A) x = 20 inches, y = 40 inches, z = 20 inches, V = 16,000 cubic inches
B) x = 20 inches, y = 20 inches, z = 17 inches, V = 6,800 cubic inches
C) x = 22 inches, y = 40 inches, z = 22 inches, V = 16,000 cubic inches
D) x = 22 inches, y = 39 inches, z = 17 inches, V = 14,586 cubic inches
E) x = 22 inches, y = 40 inches, z = 17 inches, V = 14,586 cubic inches