A rack cabinet is 15 more in front than it is in height. Side face perimeter of smallest area is 210 . You want to determine the dimensions of the rack cabinet to house and wire a communication system with a maximum volume that meet the given conditions.

a) Define suitable variables to solve the problem and obtain a mathematical expression for the volume as a function of the width of the cabinet. b) Find the maximum of the function obtained in the previous literal (argues the answer). c) Represent the function graphically and indicate the maximum point. Explain its meaning. d) Find the dimensions of the rack cabinet to establish its storage volume. maximum volume. e) Draw a figure that represents the communications rack. f) If the communications equipment (switch) have a height of 4.44 5 , How many switches can be installed in the rack while maintaining a space between them of 8, that is, between each tray?