To solve this optimization problem, we first need to translate the natural language description into a mathematical formulation. Let's denote the number of individual servings as \(x\) and the number of family servings as \(y\).

The objective is to maximize profit. Given that each individual serving is sold for a profit of $3 and each family serving is sold for a profit of $10, the total profit can be represented by the equation:
\[ \text{Profit} = 3x + 10y \]

There are several constraints based on the problem description:

1. **Total Volume Constraint**: The total volume of soup used should not exceed 50,000 ml. Given that an individual serving has 250 ml and a family serving has 1200 ml, this constraint can be written as:
\[ 250x + 1200y \leq 50000 \]

2. **Individual Servings Constraint**: The number of individual servings must be at least three times the number of family servings:
\[ x \geq 3y \]

3. **Family Servings Minimum Constraint**: There must be at least 10 family servings:
\[ y \geq 10 \]

4. **Non-Negativity Constraints**: Both \(x\) and \(y\) should be non-negative since we cannot have negative servings:
\[ x \geq 0, y \geq 0 \]
And since these are quantities of servings, they must also be integers, but for simplicity in finding the optimal solution using linear programming, we'll initially solve this as a continuous problem and then consider integer solutions if necessary.

Now, let's translate this into Gurobi code:

```python
from gurobipy import *

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

# Define variables
x = m.addVar(name="individual_servings", vtype=GRB.CONTINUOUS)
y = m.addVar(name="family_servings", vtype=GRB.CONTINUOUS)

# Set objective function: Maximize profit
m.setObjective(3*x + 10*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(250*x + 1200*y <= 50000, name="total_volume")
m.addConstr(x >= 3*y, name="individual_servings_minimum")
m.addConstr(y >= 10, name="family_servings_minimum")
m.addConstr(x >= 0, name="non_negative_individual")
m.addConstr(y >= 0, name="non_negative_family")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal individual servings: {x.x}")
    print(f"Optimal family servings: {y.x}")
    print(f"Max Profit: {m.ObjVal}")
else:
    print("No optimal solution found")

```
```python
from gurobipy import *

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

# Define variables
x = m.addVar(name="individual_servings", vtype=GRB.INTEGER)
y = m.addVar(name="family_servings", vtype=GRB.INTEGER)

# Set objective function: Maximize profit
m.setObjective(3*x + 10*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(250*x + 1200*y <= 50000, name="total_volume")
m.addConstr(x >= 3*y, name="individual_servings_minimum")
m.addConstr(y >= 10, name="family_servings_minimum")
m.addConstr(x >= 0, name="non_negative_individual")
m.addConstr(y >= 0, name="non_negative_family")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal individual servings: {x.x}")
    print(f"Optimal family servings: {y.x}")
    print(f"Max Profit: {m.ObjVal}")
else:
    print("No optimal solution found")
```