A sporting goods manufacturer makes two types of soccer ball, a professional standard ball (on which they make $5 profit) and a college standard ball (which generates $4 in profit). Constraints affecting production are the production capacities within three separate departments; Cutting/Dyeing, Sewing, Inspection/Packaging. Each professional ball requires 12 minutes of cutting and dyeing, 6 minutes of sewing, and 5 minutes of inspection and packaging. Each college ball requires 8 minutes of cutting and dyeing, 12 minutes of sewing, and 5 minutes of inspection and packaging. The monthly capacity for the 3 departments is as follows; Cutting/Dyeing 340 hours, Sewing 420 hours, Inspection/Packaging 184 hours. How many of each type of ball should the manufacturer produce per month in order to maximize profit?

Let P represent the number of professional balls produced and C represent the number of college balls produced.

Select all of the following that are constraints of this linear program (including the non-negativity constraints).