Question

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 2 hours to finish. Each Homer-Hitter sold makes a profit
of $17. The Big Timber takes 5 hours to trim and 5 hours to finish, and its profit is $29. The total time
available for trimming is up to 80 hours. The total available time for finishing is up to 50 hours. Find the
number of each type of bat that should be made in order to maximize their profit.

Answer 1

To maximize profit, set up a system of linear equations using the given information. Graph the constraints to find the feasible region and evaluate the objective function at each corner point to determine the maximum profit.

Step-by-step explanation:

To find the number of each type of baseball bat that should be made to maximize profit, we can set up a system of linear equations. Let's represent the number of Homer-Hitter bats as 'x' and the number of BigTimber bats as 'y'. We want to maximize the profit, so our objective function is P = 17x + 29y.

Subject to the constraints:

8x + 5y ≤ 80 (trimming time constraint)

2x + 5y ≤ 50 (finishing time constraint)

x ≥ 0 and y ≥ 0 (non-negativity constraint)

We can graph these constraints and find the feasible region. Then, we can evaluate the objective function at each corner point of the feasible region to find the maximum profit. The corner point that maximizes the profit will give us the number of each type of bat to produce.