Billy Penny is trying to determine how many units of two types of lawn mowers to produce each day. One of these is the Deluxe model, while the other is the Standard model. The profit per unit on the Deluxe model is $40, while the profit per unit on the Standard model is $60. The Deluxe model requires 30 minutes of assembly time, while the Standard model requires 20 minutes of assembly time. The Deluxe model requires 15 minutes of inspection time, while the Standard model requires 10 minutes of inspection time. The Deluxe model requires 15 minutes of packaging time, while the Standard model requires 20 minutes of packaging time. There are 450 minutes of assembly time, 180 minutes of inspection time and 300 minutes of packaging time available each day.

1. What is the linear programming model for this problem?
2. What are the boundary points of the feasible region?
3. What is the profitability at each boundary point of the feasible region?
4. How many units of each product should be manufactured to maximize profits?
5. Will there be excess capacity in any resource? If so, how much excess capacity?