Superbats, Inc., manufactures two different quality of wood baseball bats, the Wallbanger and the Dingbat. The Wallbanger takes 8 hours to trim and turn on a lathe and 2 hours to finish it. It has a profit of $17. The Dingbat takes 5 hours to trim and turn on a lathe and 5 hours to finish, but its profit is $29. The total time per day available for trimming and lathing is 80 hours and for finishing is 50 hours.

I don't see a question.

Jeb has to pay a plumber

$65 to come to his house
and $40 per hour after that.
Write an equation for the
cost (y) based on the
number of hours (x)

To solve this problem, we can use linear programming to maximize the profit.

Let x represent the number of Wallbanger bats produced daily.
Let y represent the number of Dingbat bats produced daily.

We want to maximize the total profit, which is given by the function P = 17x + 29y.

There are two constraints:
1) The total time for trimming and turning on a lathe is limited to 80 hours: 8x + 5y ≤ 80
2) The total time for finishing is limited to 50 hours: 2x + 5y ≤ 50

We also have non-negativity constraints: x, y ≥ 0.

To find the optimal solution, we need to solve this linear programming problem using one of the methods such as the Simplex method or the graphical method.

Let's use the graphical method to solve this problem.

Step 1: Graph the Constraints
Plot the lines for the two constraints on a graph. To do this, we first rewrite the inequalities as equations and plot the corresponding lines.

For the first constraint, 8x + 5y ≤ 80, rewrite it as 8x + 5y = 80.
For the second constraint, 2x + 5y ≤ 50, rewrite it as 2x + 5y = 50.

Plot the lines for these two equations on a graph. Note that the feasible region (the area that satisfies both constraints) will be the region where the lines intersect or overlap.

Step 2: Identify Feasible Region
Shade the area that satisfies both constraints. This will represent the feasible region for our problem.

Step 3: Identify Corners of the Feasible Region
Locate the corners (or vertices) of the feasible region. Each corner represents a potential solution to the problem.

Step 4: Evaluate Objective Function at Each Corner
Calculate the value of the objective function P = 17x + 29y at each corner. The corner with the highest objective function value will give us the optimal solution.

Once we find the optimal solution, we can determine the number of Wallbanger bats and Dingbat bats to produce daily in order to maximize the profit.