To solve this optimization problem, we need to maximize the exposure of the product given a budget constraint and limitations on the number of advertisements. The decision variables are the number of newspaper advertisements (`x`) and the number of television advertisements (`y`). 

The objective function is to maximize the total exposure, which can be represented as `30000x + 50000y`, since each newspaper advertisement reaches 30,000 readers and each television advertisement reaches 50,000 viewers.

There are constraints based on the budget and the minimum and maximum number of advertisements for each medium:
1. Budget constraint: `2500x + 5000y <= 200000`
2. Minimum and maximum number of newspaper advertisements: `12 <= x <= 24`
3. Minimum number of television advertisements: `y >= 10`

Given that we are dealing with a linear programming problem, we can use Gurobi to find the optimal solution.

```python
from gurobipy import *

# Create a new model
m = Model("Beverage_Company")

# Define variables
x = m.addVar(lb=12, ub=24, vtype=GRB.INTEGER, name="newspaper_advertisements")
y = m.addVar(lb=10, vtype=GRB.INTEGER, name="television_advertisements")

# Set the objective function
m.setObjective(30000*x + 50000*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(2500*x + 5000*y <= 200000, "budget_constraint")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of newspaper advertisements: {x.x}")
    print(f"Number of television advertisements: {y.x}")
    print(f"Maximum exposure: {m.objVal}")
else:
    print("No optimal solution found")
```