## Step 1: Define the symbolic representation of the variables
The variables are 'grams of carbohydrates', 'milligrams of vitamin B7', and 'milligrams of calcium'. Let's denote them as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $3.05x_1^2 + 4.9x_1x_2 + 2.29x_1x_3 + 6.35x_2^2 + 5.97x_2x_3 + 7.42x_3^2 + 3.68x_1 + 5.63x_2 + 9.44x_3$.

## 3: List the semi-algebraic constraints
The constraints are:
- $x_1 \geq 0$, $x_2 \geq 0$, $x_3 \geq 0$ (non-negativity constraints, though not explicitly stated, they are implied for quantities)
- $5x_2 + 6x_3 \geq 33$
- $7x_1 + 5x_2 \geq 43$
- $7^2x_1 + 5^2x_2 + 6^2x_3 \geq 31$
- $7x_1 + 5x_2 + 6x_3 \geq 31$
- $16^2x_2 + 13^2x_3 \geq 30$
- $9^2x_1 + 13^2x_3 \geq 39$
- $9x_1 + 16x_2 + 13x_3 \geq 67$
- $14^2x_1 + 3^2x_2 \geq 55$
- $14^2x_1 + 23^2x_3 \geq 37$
- $14x_1 + 3x_2 + 23x_3 \geq 37$
- $8^2x_1 + 26^2x_2 \geq 34$
- $8x_1 + 8x_3 \geq 42$
- $26x_2 + 8x_3 \geq 47$
- $8x_1 + 26x_2 + 8x_3 \geq 50$
- $2x_1 - x_3 \geq 0$
- $4x_2 - 7x_3 \geq 0$
- $7x_1 + 6x_3 \leq 85$
- $7x_1 + 5x_2 \leq 87$
- $16x_2 + 13x_3 \leq 219$
- $9x_1 + 13x_3 \leq 130$
- $3x_2 + 23x_3 \leq 209$
- $14x_1 + 23x_3 \leq 109$

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [('x1', 'grams of carbohydrates'), ('x2', 'milligrams of vitamin B7'), ('x3', 'milligrams of calcium')],
    'objective_function': '3.05*x1^2 + 4.9*x1*x2 + 2.29*x1*x3 + 6.35*x2^2 + 5.97*x2*x3 + 7.42*x3^2 + 3.68*x1 + 5.63*x2 + 9.44*x3',
    'constraints': [
        '5*x2 + 6*x3 >= 33',
        '7*x1 + 5*x2 >= 43',
        '49*x1 + 25*x2 + 36*x3 >= 31',
        '7*x1 + 5*x2 + 6*x3 >= 31',
        '256*x2 + 169*x3 >= 30',
        '81*x1 + 169*x3 >= 39',
        '9*x1 + 16*x2 + 13*x3 >= 67',
        '196*x1 + 9*x2 >= 55',
        '196*x1 + 529*x3 >= 37',
        '14*x1 + 3*x2 + 23*x3 >= 37',
        '64*x1 + 676*x2 >= 34',
        '8*x1 + 8*x3 >= 42',
        '26*x2 + 8*x3 >= 47',
        '8*x1 + 26*x2 + 8*x3 >= 50',
        '2*x1 - x3 >= 0',
        '4*x2 - 7*x3 >= 0',
        '7*x1 + 6*x3 <= 85',
        '7*x1 + 5*x2 <= 87',
        '16*x2 + 13*x3 <= 219',
        '9*x1 + 13*x3 <= 130',
        '3*x2 + 23*x3 <= 209',
        '14*x1 + 23*x3 <= 109'
    ]
}
```

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

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name="carbohydrates", lb=0)  # grams of carbohydrates
    x2 = model.addVar(name="vitamin_B7", lb=0)  # milligrams of vitamin B7
    x3 = model.addVar(name="calcium", lb=0)  # milligrams of calcium

    # Objective function
    model.setObjective(3.05*x1**2 + 4.9*x1*x2 + 2.29*x1*x3 + 6.35*x2**2 + 5.97*x2*x3 + 7.42*x3**2 + 3.68*x1 + 5.63*x2 + 9.44*x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(5*x2 + 6*x3 >= 33)
    model.addConstr(7*x1 + 5*x2 >= 43)
    model.addConstr(49*x1 + 25*x2 + 36*x3 >= 31)
    model.addConstr(7*x1 + 5*x2 + 6*x3 >= 31)
    model.addConstr(256*x2 + 169*x3 >= 30)
    model.addConstr(81*x1 + 169*x3 >= 39)
    model.addConstr(9*x1 + 16*x2 + 13*x3 >= 67)
    model.addConstr(196*x1 + 9*x2 >= 55)
    model.addConstr(196*x1 + 529*x3 >= 37)
    model.addConstr(14*x1 + 3*x2 + 23*x3 >= 37)
    model.addConstr(64*x1 + 676*x2 >= 34)
    model.addConstr(8*x1 + 8*x3 >= 42)
    model.addConstr(26*x2 + 8*x3 >= 47)
    model.addConstr(8*x1 + 26*x2 + 8*x3 >= 50)
    model.addConstr(2*x1 - x3 >= 0)
    model.addConstr(4*x2 - 7*x3 >= 0)
    model.addConstr(7*x1 + 6*x3 <= 85)
    model.addConstr(7*x1 + 5*x2 <= 87)
    model.addConstr(16*x2 + 13*x3 <= 219)
    model.addConstr(9*x1 + 13*x3 <= 130)
    model.addConstr(3*x2 + 23*x3 <= 209)
    model.addConstr(14*x1 + 23*x3 <= 109)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Carbohydrates: {x1.varValue}")
        print(f"Vitamin B7: {x2.varValue}")
        print(f"Calcium: {x3.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```