To solve Emma's dietary problem using linear programming, we first need to define the variables and the objective function. Let's denote:
- $x_1$ as the number of units of pork Emma eats.
- $x_2$ as the number of units of shrimp Emma eats.

The objective is to minimize the total cost of the diet. Given that pork costs $3 per unit and shrimp costs $5.5 per unit, the objective function can be represented as:
\[ \text{Minimize} \quad 3x_1 + 5.5x_2 \]

Now, let's formulate the constraints based on Emma's nutritional requirements:
1. The diet must include a minimum of 120 units of proteins.
2. The diet must include a minimum of 30 units of fat.

Given that one unit of pork has 15 units of proteins and 4 units of fat, and one unit of shrimp has 22 units of proteins and 7 units of fat, we can represent these constraints as:
\[ 15x_1 + 22x_2 \geq 120 \] (Protein constraint)
\[ 4x_1 + 7x_2 \geq 30 \] (Fat constraint)

Additionally, since Emma cannot eat a negative amount of food, we have non-negativity constraints:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'units of pork'), ('x2', 'units of shrimp')],
    'objective_function': '3*x1 + 5.5*x2',
    'constraints': ['15*x1 + 22*x2 >= 120', '4*x1 + 7*x2 >= 30', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we can use the following code:

```python
from gurobipy import *

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

# Add variables to the model
x1 = m.addVar(lb=0, name="pork")
x2 = m.addVar(lb=0, name="shrimp")

# Set the objective function
m.setObjective(3*x1 + 5.5*x2, GRB.MINIMIZE)

# Add constraints to the model
m.addConstr(15*x1 + 22*x2 >= 120, "Protein_Constraint")
m.addConstr(4*x1 + 7*x2 >= 30, "Fat_Constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Units of pork: {x1.x}")
    print(f"Units of shrimp: {x2.x}")
    print(f"Total cost: {m.objVal}")
else:
    print("No optimal solution found.")
```