Cardin Company produces two types of gears: Model #12 and Model #15. Market conditions limit the number of each gear that can be sold. For Model #12, no more than 15,000 units can be sold, and for Model #15, no more than 40,000 units. Each gear must be notched by a special machine. Cardin owns eight machines that together provide 40,000 hours of machine time per year. Each unit of Model #12 requires two hours of machine time, and each unit of Model #15 requires one half hour of machine time. The unit contribution for Model #12 is \($30\) and for Model

#15 is \($15\). Cardin wants to identify the product mix that will maximize total contribution margin.

Required:

1. Formulate Cardin’s problem as a linear programming model.

2. Solve the linear programming model in Requirement 1.

3. Identify which constraints are binding and which are loose. Also, identify the constraints as internal or external.