## Step 1: Define the optimization problem
The problem is to maximize the objective function: $2x_0 + 3x_1 + 3x_2 + 5x_3 + 9x_4$, where $x_0$ represents milligrams of vitamin B1, $x_1$ represents milligrams of vitamin B5, $x_2$ represents milligrams of vitamin B3, $x_3$ represents milligrams of vitamin B2, and $x_4$ represents milligrams of potassium.

## Step 2: List all the constraints
The constraints are as follows:
1. $13x_0 + 21x_1 \geq 46$
2. $23x_2 + 16x_3 \geq 37$
3. $21x_1 + 16x_3 \geq 33$
4. $13x_0 + 23x_2 \geq 51$
5. $21x_1 + 23x_2 \geq 59$
6. $16x_3 + 9x_4 \geq 33$
7. $13x_0 + 9x_4 \geq 53$
8. $13x_0 + 23x_2 + 16x_3 \geq 45$
9. $13x_0 + 23x_2 + 9x_4 \geq 45$
10. $21x_1 + 16x_3 + 9x_4 \geq 45$
11. $21x_1 + 23x_2 + 16x_3 \geq 45$
12. $13x_0 + 23x_2 + 16x_3 \geq 53$
13. $13x_0 + 23x_2 + 9x_4 \geq 53$
14. $21x_1 + 16x_3 + 9x_4 \geq 53$
15. $21x_1 + 23x_2 + 16x_3 \geq 53$
16. $13x_0 + 23x_2 + 16x_3 \geq 60$
17. $13x_0 + 23x_2 + 9x_4 \geq 60$
18. $21x_1 + 16x_3 + 9x_4 \geq 60$
19. $21x_1 + 23x_2 + 16x_3 \geq 60$
20. $13x_0 + 23x_2 + 16x_3 \geq 78$
21. $13x_0 + 23x_2 + 9x_4 \geq 78$
22. $21x_1 + 16x_3 + 9x_4 \geq 78$
23. $21x_1 + 23x_2 + 16x_3 \geq 78$
24. $8x_0 - 3x_1 + 10x_2 \geq 0$
25. $21x_1 + 9x_4 \leq 275$
26. $16x_3 + 9x_4 \leq 144$
27. $13x_0 + 21x_1 + 9x_4 \leq 197$
28. $13x_0 + 23x_2 + 9x_4 \leq 265$
29. $13x_0 + 21x_1 + 23x_2 + 16x_3 + 9x_4 \leq 265$

## Step 3: Implement the optimization problem using Gurobi
We will use the Gurobi library in Python to solve this linear programming problem.

```python
import gurobi

def solve_optimization_problem():
    # Create a new Gurobi model
    model = gurobi.Model()

    # Define the variables
    x0 = model.addVar(name="milligrams of vitamin B1", lb=-gurobi.GRB.INFINITY)
    x1 = model.addVar(name="milligrams of vitamin B5", lb=-gurobi.GRB.INFINITY)
    x2 = model.addVar(name="milligrams of vitamin B3", lb=-gurobi.GRB.INFINITY)
    x3 = model.addVar(name="milligrams of vitamin B2", lb=-gurobi.GRB.INFINITY)
    x4 = model.addVar(name="milligrams of potassium", lb=-gurobi.GRB.INFINITY)

    # Define the objective function
    model.setObjective(2*x0 + 3*x1 + 3*x2 + 5*x3 + 9*x4, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(13*x0 + 21*x1 >= 46)
    model.addConstr(23*x2 + 16*x3 >= 37)
    model.addConstr(21*x1 + 16*x3 >= 33)
    model.addConstr(13*x0 + 23*x2 >= 51)
    model.addConstr(21*x1 + 23*x2 >= 59)
    model.addConstr(16*x3 + 9*x4 >= 33)
    model.addConstr(13*x0 + 9*x4 >= 53)
    model.addConstr(13*x0 + 23*x2 + 16*x3 >= 45)
    model.addConstr(13*x0 + 23*x2 + 9*x4 >= 45)
    model.addConstr(21*x1 + 16*x3 + 9*x4 >= 45)
    model.addConstr(21*x1 + 23*x2 + 16*x3 >= 45)
    model.addConstr(13*x0 + 23*x2 + 16*x3 >= 53)
    model.addConstr(13*x0 + 23*x2 + 9*x4 >= 53)
    model.addConstr(21*x1 + 16*x3 + 9*x4 >= 53)
    model.addConstr(21*x1 + 23*x2 + 16*x3 >= 53)
    model.addConstr(13*x0 + 23*x2 + 16*x3 >= 60)
    model.addConstr(13*x0 + 23*x2 + 9*x4 >= 60)
    model.addConstr(21*x1 + 16*x3 + 9*x4 >= 60)
    model.addConstr(21*x1 + 23*x2 + 16*x3 >= 60)
    model.addConstr(13*x0 + 23*x2 + 16*x3 >= 78)
    model.addConstr(13*x0 + 23*x2 + 9*x4 >= 78)
    model.addConstr(21*x1 + 16*x3 + 9*x4 >= 78)
    model.addConstr(21*x1 + 23*x2 + 16*x3 >= 78)
    model.addConstr(8*x0 - 3*x1 + 10*x2 >= 0)
    model.addConstr(21*x1 + 9*x4 <= 275)
    model.addConstr(16*x3 + 9*x4 <= 144)
    model.addConstr(13*x0 + 21*x1 + 9*x4 <= 197)
    model.addConstr(13*x0 + 23*x2 + 9*x4 <= 265)
    model.addConstr(13*x0 + 21*x1 + 23*x2 + 16*x3 + 9*x4 <= 265)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print("Milligrams of vitamin B1: ", x0.varValue)
        print("Milligrams of vitamin B5: ", x1.varValue)
        print("Milligrams of vitamin B3: ", x2.varValue)
        print("Milligrams of vitamin B2: ", x3.varValue)
        print("Milligrams of potassium: ", x4.varValue)
        print("Objective function value: ", model.objVal)
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```