Solve, using first and second order optimization conditions, the following conditioned optimization problem:

A manufacturer of milk packaging (in the rectangular shape in the figure below), wants to choose its dimensions (x,y and z, in centimeters) in order to maximize the volume of its content (given by V=xyz). However, he has to satisfy the desire of the dairy cooperative, which imposes the cost of each package to be exactly $2.00. Solve the problem of the ideal dimensions of each package that your producer will choose, knowing that the cost of each package for it is composed of: $4.00 per unit area (cm²) of the top and bottom lids and $3.00 per unit area (cm²) of the sides of each package.