The Wadsworth Widget Company manufactures two types of widgets: regular and deluxe. Each widget is produced at a station consisting of a machine and a person who finishes each widget by hand. The regular widget requires \(3 \mathrm{hr}\) of machine time and \(2 \mathrm{hr}\) of finishing time. The deluxe widget requires \(2 \mathrm{hr}\) of machine time and \(4 \mathrm{hr}\) of finishing time. The profit on the regular widget is \(\$ 25\); on the deluxe widget it is \(\$ 30\). If the workday is 8 hours, how many of each type of widget should be produced at each station per day to maximize the profit?

Write a linear programming model, including the objective function and the set of constraints, for Problems 52-55. DO NOT SOLVE, but be sure to define all your variables.