$.$ Billy Penny is trying to determine how many units of two types of lawn mowers to produce

each day. One of these is the Standard model, while the other is the Deluxe model. The profit

per unit on the Standard model is $$60,$ while the profit per unit on the Deluxe model is $$40.$

The Standard model requires $18$ minutes of assembly time, while the Deluxe model requires

$12$ minutes of assembly time. The Standard model requires $10$ minutes of inspection time, while

the Deluxe model requires $15$ minutes of inspection time. There are $210$ minutes of assembly

time and $200$ minutes of inspection time available each day.

a$)$ Formulate the linear programming problem. $(10$ Points$)$

b$)$ How many units of each product should be manufactured to maximize profits using the

Corner Point Method or Isoprofit Line Solution Method? $(15$ Points$)$