## Step 1: Define the symbolic representation of the variables
The variables are 'blueberry pies', 'pickles', 'bowls of pasta', and 'sashimi', which can be represented symbolically as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to minimize is $9x_1 + 5x_2 + 1x_3 + 7x_4$.

## Step 3: List the constraints in symbolic notation
The constraints are:
1. $2x_1 + 5x_2 + 3x_3 + 7x_4 \leq 207$ (carbohydrates upper bound)
2. $2x_1 + 7x_4 \geq 36$ (carbohydrates from blueberry pies and sashimi)
3. $2x_1 + 5x_2 \geq 18$ (carbohydrates from blueberry pies and pickles)
4. $5x_2 + 3x_3 \geq 31$ (carbohydrates from pickles and bowls of pasta)
5. $3x_3 + 7x_4 \geq 24$ (carbohydrates from bowls of pasta and sashimi)
6. $5x_2 + 7x_4 \geq 47$ (carbohydrates from pickles and sashimi)
7. $2x_1 + 5x_2 + 7x_4 \geq 36$ (carbohydrates from blueberry pies, pickles, and sashimi)
8. $2x_1 + 3x_3 + 7x_4 \geq 36$ (carbohydrates from blueberry pies, bowls of pasta, and sashimi)
9. $2x_1 + 5x_2 + 3x_3 + 7x_4 \geq 43$ (carbohydrates from all)
10. $2x_1 + 5x_2 + 7x_4 \geq 43$ (carbohydrates from blueberry pies, pickles, and sashimi)
11. $2x_1 + 3x_3 + 7x_4 \geq 43$ (carbohydrates from blueberry pies, bowls of pasta, and sashimi)
12. $-2x_1 + 2x_2 \geq 0$ (relationship between blueberry pies and pickles)
13. $5x_2 + 7x_4 \leq 57$ (carbohydrates from pickles and sashimi)
14. $2x_1 + 5x_2 + 3x_3 \leq 143$ (carbohydrates from blueberry pies, pickles, and bowls of pasta)
15. $2x_1 + 3x_3 + 7x_4 \leq 181$ (carbohydrates from blueberry pies, bowls of pasta, and sashimi)
16. $5x_2 + 3x_3 + 7x_4 \leq 125$ (carbohydrates from pickles, bowls of pasta, and sashimi)

## Step 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'blueberry pies'), 
        ('x2', 'pickles'), 
        ('x3', 'bowls of pasta'), 
        ('x4', 'sashimi')
    ], 
    'objective_function': '9*x1 + 5*x2 + 1*x3 + 7*x4', 
    'constraints': [
        '2*x1 + 5*x2 + 3*x3 + 7*x4 <= 207',
        '2*x1 + 7*x4 >= 36',
        '2*x1 + 5*x2 >= 18',
        '5*x2 + 3*x3 >= 31',
        '3*x3 + 7*x4 >= 24',
        '5*x2 + 7*x4 >= 47',
        '2*x1 + 5*x2 + 7*x4 >= 36',
        '2*x1 + 3*x3 + 7*x4 >= 36',
        '2*x1 + 5*x2 + 3*x3 + 7*x4 >= 43',
        '2*x1 + 5*x2 + 7*x4 >= 43',
        '2*x1 + 3*x3 + 7*x4 >= 43',
        '-2*x1 + 2*x2 >= 0',
        '5*x2 + 7*x4 <= 57',
        '2*x1 + 5*x2 + 3*x3 <= 143',
        '2*x1 + 3*x3 + 7*x4 <= 181',
        '5*x2 + 3*x3 + 7*x4 <= 125'
    ]
}
```

## Step 5: Write the Gurobi code for the optimization problem
```python
import gurobi

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

# Define the variables
x1 = model.addVar(name='blueberry_pies', lb=0)  # No lower bound specified, assuming 0
x2 = model.addVar(name='pickles', lb=0)  # No lower bound specified, assuming 0
x3 = model.addVar(name='bowls_of_pasta', lb=0, integrality=gurobi.GRB.INTEGER)  # Integer variable
x4 = model.addVar(name='sashimi', lb=0)  # No lower bound specified, assuming 0

# Objective function
model.setObjective(9 * x1 + 5 * x2 + x3 + 7 * x4, gurobi.GRB.MINIMIZE)

# Constraints
model.addConstr(2 * x1 + 5 * x2 + 3 * x3 + 7 * x4 <= 207)
model.addConstr(2 * x1 + 7 * x4 >= 36)
model.addConstr(2 * x1 + 5 * x2 >= 18)
model.addConstr(5 * x2 + 3 * x3 >= 31)
model.addConstr(3 * x3 + 7 * x4 >= 24)
model.addConstr(5 * x2 + 7 * x4 >= 47)
model.addConstr(2 * x1 + 5 * x2 + 7 * x4 >= 36)
model.addConstr(2 * x1 + 3 * x3 + 7 * x4 >= 36)
model.addConstr(2 * x1 + 5 * x2 + 3 * x3 + 7 * x4 >= 43)
model.addConstr(2 * x1 + 5 * x2 + 7 * x4 >= 43)
model.addConstr(2 * x1 + 3 * x3 + 7 * x4 >= 43)
model.addConstr(-2 * x1 + 2 * x2 >= 0)
model.addConstr(5 * x2 + 7 * x4 <= 57)
model.addConstr(2 * x1 + 5 * x2 + 3 * x3 <= 143)
model.addConstr(2 * x1 + 3 * x3 + 7 * x4 <= 181)
model.addConstr(5 * x2 + 3 * x3 + 7 * x4 <= 125)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', model.objVal)
    print('Blueberry pies: ', x1.varValue)
    print('Pickles: ', x2.varValue)
    print('Bowls of pasta: ', x3.varValue)
    print('Sashimi: ', x4.varValue)
else:
    print('The model is infeasible')
```