Superbats Inc. manufactures two different types of wood baseball bats, the Homer-Hitter and the Big Timber. The Homer-Hitter takes 8 hours to trim and turn on the lathe and 2 hours to finish. Each Homer-Hitter sold makes a profit of $17. The Big Timber takes 5 hours to trim and turn on the lathe and 5 hours to finish, and its profit is $29. The total time available for trimming and lathing is 80 hours. The total available time for finishing is 50 hours.

(a) What are your variables and what do they represent?

(b) Write the objective quantity equation.

(c) Write the system of inequalities that describes the constraints.

(d) Graph the system of inequalities and find the vertices.

(e) How many of each type should be produced in order to maximize their profit? What is the maximum profit?