Burnett 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. Burnett owns eight machines that together provide 60,000 hours of machine time per year. Each unit of Model 12 requires three hours of machine time, and each unit of Model 15 requires 45 minutes or 0.75 hour of machine time. The unit contribution for Model 12 is $60 and for Model 15 is $30. Burnett wants to identify the product mix that will maximize total contribution margin.
Required:
1. Formulate Burnett’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.