Suppose a Home Improvement Contractor Is Painting the Walls and Ceiling

Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 360 cubic feet. The cost of wall paint is $0.054 per square foot and the cost of ceiling paint is $0.18 per square foot. Let x, y, and z be the length, width, and height of a rectangular room respectively. Identify the room dimensions that result in a minimum cost for the paint and use these dimensions to find the minimum cost for the paint. Round your answer to the nearest cent.

A) $54.00
B) $8.64
C) $7.00
D) $19.44
E) $21.60