## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to several constraints. The variables are:
- $x_1$: milligrams of vitamin K
- $x_2$: milligrams of zinc
- $x_3$: milligrams of potassium

The objective function to minimize is: $3x_1 + 2x_2 + 8x_3$

## Step 2: List the constraints
The constraints given are:
- $2.2x_1 \leq 71$
- $3.99x_1 \leq 61$
- $0.26x_1 \leq 64$
- $0.26x_2 \leq 71$
- $2.9x_2 \leq 61$
- $0.79x_2 \leq 64$
- $2.58x_3 \leq 71$
- $2.61x_3 \leq 61$
- $4.67x_3 \leq 64$
- $2.2x_1 + 0.26x_2 \geq 22$
- $0.26x_2 + 2.58x_3 \geq 13$
- $2.2x_1 + 0.26x_2 + 2.58x_3 \geq 13$
- $3.99x_1 + 2.9x_2 \geq 13$
- $3.99x_1 + 2.61x_3 \geq 12$
- $3.99x_1 + 2.9x_2 + 2.61x_3 \geq 11$
- $0.79x_2 + 4.67x_3 \geq 8$
- $0.26x_1 + 0.79x_2 \geq 14$
- $0.26x_1 + 0.79x_2 + 4.67x_3 \geq 14$
- $3x_2 - 7x_3 \geq 0$
- $2.9x_2 + 2.61x_3 \leq 38$
- $3.99x_1 + 2.9x_2 \leq 22$
- $x_1$ is an integer
- $x_2$ can be any real number
- $x_3$ can be any real number

## Step 3: Convert the problem into Gurobi code
We will use the Gurobi Python API to model and solve this problem.

```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x1 = m.addVar(name="x1", vtype=gp.GRB.INTEGER)  # milligrams of vitamin K
x2 = m.addVar(name="x2")  # milligrams of zinc
x3 = m.addVar(name="x3")  # milligrams of potassium

# Define the objective function
m.setObjective(3*x1 + 2*x2 + 8*x3, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(2.2*x1 <= 71)
m.addConstr(3.99*x1 <= 61)
m.addConstr(0.26*x1 <= 64)
m.addConstr(0.26*x2 <= 71)
m.addConstr(2.9*x2 <= 61)
m.addConstr(0.79*x2 <= 64)
m.addConstr(2.58*x3 <= 71)
m.addConstr(2.61*x3 <= 61)
m.addConstr(4.67*x3 <= 64)
m.addConstr(2.2*x1 + 0.26*x2 >= 22)
m.addConstr(0.26*x2 + 2.58*x3 >= 13)
m.addConstr(2.2*x1 + 0.26*x2 + 2.58*x3 >= 13)
m.addConstr(3.99*x1 + 2.9*x2 >= 13)
m.addConstr(3.99*x1 + 2.61*x3 >= 12)
m.addConstr(3.99*x1 + 2.9*x2 + 2.61*x3 >= 11)
m.addConstr(0.79*x2 + 4.67*x3 >= 8)
m.addConstr(0.26*x1 + 0.79*x2 >= 14)
m.addConstr(0.26*x1 + 0.79*x2 + 4.67*x3 >= 14)
m.addConstr(3*x2 - 7*x3 >= 0)
m.addConstr(2.9*x2 + 2.61*x3 <= 38)
m.addConstr(3.99*x1 + 2.9*x2 <= 22)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Milligrams of vitamin K: {x1.varValue}")
    print(f"Milligrams of zinc: {x2.varValue}")
    print(f"Milligrams of potassium: {x3.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```

## Step 4: Symbolic representation of the problem
The symbolic representation is as follows:

```json
{
    'sym_variables': [
        ('x1', 'milligrams of vitamin K'),
        ('x2', 'milligrams of zinc'),
        ('x3', 'milligrams of potassium')
    ],
    'objective_function': '3*x1 + 2*x2 + 8*x3',
    'constraints': [
        '2.2*x1 <= 71',
        '3.99*x1 <= 61',
        '0.26*x1 <= 64',
        '0.26*x2 <= 71',
        '2.9*x2 <= 61',
        '0.79*x2 <= 64',
        '2.58*x3 <= 71',
        '2.61*x3 <= 61',
        '4.67*x3 <= 64',
        '2.2*x1 + 0.26*x2 >= 22',
        '0.26*x2 + 2.58*x3 >= 13',
        '2.2*x1 + 0.26*x2 + 2.58*x3 >= 13',
        '3.99*x1 + 2.9*x2 >= 13',
        '3.99*x1 + 2.61*x3 >= 12',
        '3.99*x1 + 2.9*x2 + 2.61*x3 >= 11',
        '0.79*x2 + 4.67*x3 >= 8',
        '0.26*x1 + 0.79*x2 >= 14',
        '0.26*x1 + 0.79*x2 + 4.67*x3 >= 14',
        '3*x2 - 7*x3 >= 0',
        '2.9*x2 + 2.61*x3 <= 38',
        '3.99*x1 + 2.9*x2 <= 22'
    ]
}
```