A private hospital offers three types of health check-up packages: basic, vital, and advanced packages. The profit from these is estimated as $310 per unit for basic packages, $270 per unit for vital packages, and $430 per unit for advanced packages. Basic packages require 2 hours of testing and 5 hours of consultation per unit; vital packages require 1 hour of testing and 4 hours of consultation per unit; advanced packages require 3 hours of testing and 6 hours of consultation per unit. Currently, the available number of testing hours is 180 and the available number of consultation hours is 360. The hospital manager wishes to establish the sales quotas for each of the three types to maximize the total profit. These quotas are assumed to be continuous quantities, so they can take fractional values. The manager requires at most 60% of the total sales quotas to consist of basic packages. Formulate this problem as a linear program by defining the decision variables, the objective function, and the constraints. [Do not solve it.]