## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of vitamin D', 'milligrams of potassium', 'milligrams of vitamin K'], which we can denote as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- $x_0$ : milligrams of vitamin D
- $x_1$ : milligrams of potassium
- $x_2$ : milligrams of vitamin K

## Step 3: Define the objective function in symbolic notation
The objective function to minimize is $8x_0 + 3x_1 + 1x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $3x_0 \leq 22$
- $3x_0 \leq 50$
- $3x_0 \leq 18$
- $1x_0 \leq 19$
- $1x_0 \leq 25$
- $3x_1 \leq 22$
- $5x_1 \leq 50$
- $2x_1 \leq 18$
- $1x_1 \leq 19$
- $5x_1 \leq 25$
- $1x_2 \leq 22$
- $5x_2 \leq 50$
- $5x_2 \leq 18$
- $4x_2 \leq 19$
- $2x_2 \leq 25$
- $3x_0 + 3x_1 \geq 2$
- $3x_1 + 1x_2 \geq 7$
- $3x_0 + 3x_1 + 1x_2 \geq 7$
- $5x_1 + 5x_2 \geq 6$
- $3x_0 + 5x_2 \geq 9$
- $3x_0 + 5x_1 + 5x_2 \geq 9$
- $3x_0 + 5x_2 \geq 3$
- $2x_1 + 5x_2 \geq 4$
- $3x_0 + 2x_1 + 5x_2 \geq 6$
- $3x_0 + 2x_1 + 5x_2 \geq 6$
- $1x_1 + 4x_2 \geq 2$
- $1x_0 + 4x_2 \geq 6$
- $1x_0 + 1x_1 + 4x_2 \geq 5$
- $1x_0 + 1x_1 + 4x_2 \geq 5$
- $5x_1 + 2x_2 \geq 4$
- $1x_0 + 5x_1 \geq 2$
- $1x_0 + 5x_1 + 2x_2 \geq 8$
- $1x_0 + 5x_1 + 2x_2 \geq 8$
- $-7x_0 + 8x_1 \geq 0$
- $-7x_0 + 2x_2 \geq 0$
- $3x_0 + 2x_1 + 5x_2 \leq 14$
- $1x_0 + 1x_1 + 4x_2 \leq 10$
- $1x_0 + 2x_2 \leq 15$
- $5x_1 + 2x_2 \leq 13$

## 5: Define the variable types
- $x_0$ is an integer (nonfractional number of milligrams of vitamin D)
- $x_1$ is a continuous variable (non-integer amount of milligrams of potassium)
- $x_2$ is an integer (integer number of milligrams of vitamin K)

## 6: Write the Gurobi code
```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin D
x1 = model.addVar(name="x1", vtype=gurobi.GRB.CONTINUOUS)  # milligrams of potassium
x2 = model.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin K

# Objective function
model.setObjective(8 * x0 + 3 * x1 + x2, gurobi.GRB.MINIMIZE)

# Constraints
model.addConstr(3 * x0 <= 22, name="c1")
model.addConstr(3 * x0 <= 50, name="c2")
model.addConstr(3 * x0 <= 18, name="c3")
model.addConstr(x0 <= 19, name="c4")
model.addConstr(x0 <= 25, name="c5")

model.addConstr(3 * x1 <= 22, name="c6")
model.addConstr(5 * x1 <= 50, name="c7")
model.addConstr(2 * x1 <= 18, name="c8")
model.addConstr(x1 <= 19, name="c9")
model.addConstr(5 * x1 <= 25, name="c10")

model.addConstr(x2 <= 22, name="c11")
model.addConstr(5 * x2 <= 50, name="c12")
model.addConstr(5 * x2 <= 18, name="c13")
model.addConstr(4 * x2 <= 19, name="c14")
model.addConstr(2 * x2 <= 25, name="c15")

model.addConstr(3 * x0 + 3 * x1 >= 2, name="c16")
model.addConstr(3 * x1 + x2 >= 7, name="c17")
model.addConstr(3 * x0 + 3 * x1 + x2 >= 7, name="c18")
model.addConstr(5 * x1 + 5 * x2 >= 6, name="c19")
model.addConstr(3 * x0 + 5 * x2 >= 9, name="c20")
model.addConstr(3 * x0 + 5 * x1 + 5 * x2 >= 9, name="c21")

model.addConstr(3 * x0 + 5 * x2 >= 3, name="c22")
model.addConstr(2 * x1 + 5 * x2 >= 4, name="c23")
model.addConstr(3 * x0 + 2 * x1 + 5 * x2 >= 6, name="c24")

model.addConstr(x1 + 4 * x2 >= 2, name="c25")
model.addConstr(x0 + 4 * x2 >= 6, name="c26")
model.addConstr(x0 + x1 + 4 * x2 >= 5, name="c27")

model.addConstr(5 * x1 + 2 * x2 >= 4, name="c28")
model.addConstr(x0 + 5 * x1 >= 2, name="c29")
model.addConstr(x0 + 5 * x1 + 2 * x2 >= 8, name="c30")

model.addConstr(-7 * x0 + 8 * x1 >= 0, name="c31")
model.addConstr(-7 * x0 + 2 * x2 >= 0, name="c32")

model.addConstr(3 * x0 + 2 * x1 + 5 * x2 <= 14, name="c33")
model.addConstr(x0 + x1 + 4 * x2 <= 10, name="c34")
model.addConstr(x0 + 2 * x2 <= 15, name="c35")
model.addConstr(5 * x1 + 2 * x2 <= 13, name="c36")

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objval)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 7: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin D'), 
        ('x1', 'milligrams of potassium'), 
        ('x2', 'milligrams of vitamin K')
    ], 
    'objective_function': '8*x0 + 3*x1 + x2', 
    'constraints': [
        '3*x0 <= 22', 
        '3*x0 <= 50', 
        '3*x0 <= 18', 
        'x0 <= 19', 
        'x0 <= 25', 
        '3*x1 <= 22', 
        '5*x1 <= 50', 
        '2*x1 <= 18', 
        'x1 <= 19', 
        '5*x1 <= 25', 
        'x2 <= 22', 
        '5*x2 <= 50', 
        '5*x2 <= 18', 
        '4*x2 <= 19', 
        '2*x2 <= 25', 
        '3*x0 + 3*x1 >= 2', 
        '3*x1 + x2 >= 7', 
        '3*x0 + 3*x1 + x2 >= 7', 
        '5*x1 + 5*x2 >= 6', 
        '3*x0 + 5*x2 >= 9', 
        '3*x0 + 5*x1 + 5*x2 >= 9', 
        '3*x0 + 5*x2 >= 3', 
        '2*x1 + 5*x2 >= 4', 
        '3*x0 + 2*x1 + 5*x2 >= 6', 
        'x1 + 4*x2 >= 2', 
        'x0 + 4*x2 >= 6', 
        'x0 + x1 + 4*x2 >= 5', 
        '5*x1 + 2*x2 >= 4', 
        'x0 + 5*x1 >= 2', 
        'x0 + 5*x1 + 2*x2 >= 8', 
        '-7*x0 + 8*x1 >= 0', 
        '-7*x0 + 2*x2 >= 0', 
        '3*x0 + 2*x1 + 5*x2 <= 14', 
        'x0 + x1 + 4*x2 <= 10', 
        'x0 + 2*x2 <= 15', 
        '5*x1 + 2*x2 <= 13'
    ]
}
```