## Step 1: Define the symbolic representation of the problem
The problem involves three variables: 'bowls of pasta', 'steaks', and 'blueberry pies', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $1 \cdot x_0 + 5 \cdot x_1 + 1 \cdot x_2$.

## 3: List the semi-algebraic constraints
The constraints given are:
- $2.81x_1 + 2.51x_2 \geq 65$
- $1.58x_0 + 2.81x_1 + 2.51x_2 \geq 65$
- $1.4x_0 + 3.08x_2 \geq 54$
- $1.4x_0 + 3.27x_1 \geq 106$
- $1.4x_0 + 3.27x_1 + 3.08x_2 \geq 138$
- $1.4x_0 + 3.51x_1 \geq 124$
- $1.4x_0 + 3.13x_2 \geq 118$
- $3.51x_1 + 3.13x_2 \geq 135$
- $2.85x_0 + 3.51x_1 + 3.13x_2 \geq 135$
- $3.9x_0 + 3.81x_2 \geq 53$
- $3.9x_0 + 2.12x_1 + 3.81x_2 \geq 48$
- $2.71x_1 + 1.78x_2 \geq 75$
- $0.73x_0 + 2.71x_1 + 1.78x_2 \geq 75$
- $2x_0 - 2x_1 \geq 0$
- $1.58x_0 + 2.81x_1 \leq 370$
- $2.12x_1 + 3.81x_2 \leq 127$

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [('x0', 'bowls of pasta'), ('x1', 'steaks'), ('x2', 'blueberry pies')],
    'objective_function': '1*x0 + 5*x1 + 1*x2',
    'constraints': [
        '2.81*x1 + 2.51*x2 >= 65',
        '1.58*x0 + 2.81*x1 + 2.51*x2 >= 65',
        '1.4*x0 + 3.08*x2 >= 54',
        '1.4*x0 + 3.27*x1 >= 106',
        '1.4*x0 + 3.27*x1 + 3.08*x2 >= 138',
        '1.4*x0 + 3.51*x1 >= 124',
        '1.4*x0 + 3.13*x2 >= 118',
        '3.51*x1 + 3.13*x2 >= 135',
        '2.85*x0 + 3.51*x1 + 3.13*x2 >= 135',
        '3.9*x0 + 3.81*x2 >= 53',
        '3.9*x0 + 2.12*x1 + 3.81*x2 >= 48',
        '2.71*x1 + 1.78*x2 >= 75',
        '0.73*x0 + 2.71*x1 + 1.78*x2 >= 75',
        '2*x0 - 2*x1 >= 0',
        '1.58*x0 + 2.81*x1 <= 370',
        '2.12*x1 + 3.81*x2 <= 127'
    ]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

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

# Define the variables
x0 = model.addVar(name="bowls_of_pasta", lb=-gurobi.GRB.INFINITY)
x1 = model.addVar(name="steaks", lb=-gurobi.GRB.INFINITY)
x2 = model.addVar(name="blueberry_pies", lb=-gurobi.GRB.INFINITY)

# Set the objective function
model.setObjective(1 * x0 + 5 * x1 + 1 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(2.81 * x1 + 2.51 * x2 >= 65)
model.addConstr(1.58 * x0 + 2.81 * x1 + 2.51 * x2 >= 65)
model.addConstr(1.4 * x0 + 3.08 * x2 >= 54)
model.addConstr(1.4 * x0 + 3.27 * x1 >= 106)
model.addConstr(1.4 * x0 + 3.27 * x1 + 3.08 * x2 >= 138)
model.addConstr(1.4 * x0 + 3.51 * x1 >= 124)
model.addConstr(1.4 * x0 + 3.13 * x2 >= 118)
model.addConstr(3.51 * x1 + 3.13 * x2 >= 135)
model.addConstr(2.85 * x0 + 3.51 * x1 + 3.13 * x2 >= 135)
model.addConstr(3.9 * x0 + 3.81 * x2 >= 53)
model.addConstr(3.9 * x0 + 2.12 * x1 + 3.81 * x2 >= 48)
model.addConstr(2.71 * x1 + 1.78 * x2 >= 75)
model.addConstr(0.73 * x0 + 2.71 * x1 + 1.78 * x2 >= 75)
model.addConstr(2 * x0 - 2 * x1 >= 0)
model.addConstr(1.58 * x0 + 2.81 * x1 <= 370)
model.addConstr(2.12 * x1 + 3.81 * x2 <= 127)

# Solve the model
model.optimize()

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