## Step 1: Define the symbolic representation of the variables
The variables are ['strips of bacon', 'cornichons', 'slices of pizza', 'ham sandwiches', 'kiwis'] which can be represented symbolically as $x_0, x_1, x_2, x_3, x_4$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $3x_0 + 7x_1 + 4x_2 + 5x_3 + 7x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
- $0.56x_1 + 2.69x_2 \geq 16$
- $2.69x_2 + 2.56x_3 \geq 14$
- $1.35x_0 + 0.56x_1 + 2.69x_2 + 2.56x_3 + 1.05x_4 \geq 14$
- $0.03x_0 + 1.67x_1 \geq 11$
- $0.03x_0 + 2.17x_4 \geq 13$
- $0.03x_0 + 1.67x_1 + 2.47x_2 + 0.59x_3 + 2.17x_4 \geq 13$
- $10x_0 - 5x_1 \geq 0$
- $1.35x_0 + 2.56x_3 \leq 19$
- $0.56x_1 + 2.69x_2 + 1.05x_4 \leq 23$
- $1.35x_0 + 2.56x_3 + 1.05x_4 \leq 60$
- $1.67x_1 + 2.17x_4 \leq 59$
- $1.67x_1 + 2.47x_2 \leq 40$
- $0.03x_0 + 1.67x_1 \leq 161$
- $0.59x_3 + 2.17x_4 \leq 60$
- $0.03x_0 + 0.59x_3 \leq 127$
- $0.03x_0 + 1.67x_1 + 2.17x_4 \leq 57$

## 4: Determine the variable bounds
- $x_0$ is continuous
- $x_1$ is integer
- $x_2$ is continuous
- $x_3$ is continuous
- $x_4$ is continuous

## 5: Formulate the problem in Gurobi
We will use Gurobi to solve this optimization problem.

```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="strips_of_bacon", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)
x1 = m.addVar(name="cornichons", lb=0, ub=gp.GRB.INFINITY, integrality=gp.GRB.INTEGER)
x2 = m.addVar(name="slices_of_pizza", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)
x3 = m.addVar(name="ham_sandwiches", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)
x4 = m.addVar(name="kiwis", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)

# Define the objective function
m.setObjective(3*x0 + 7*x1 + 4*x2 + 5*x3 + 7*x4, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(0.56*x1 + 2.69*x2 >= 16)
m.addConstr(2.69*x2 + 2.56*x3 >= 14)
m.addConstr(1.35*x0 + 0.56*x1 + 2.69*x2 + 2.56*x3 + 1.05*x4 >= 14)
m.addConstr(0.03*x0 + 1.67*x1 >= 11)
m.addConstr(0.03*x0 + 2.17*x4 >= 13)
m.addConstr(0.03*x0 + 1.67*x1 + 2.47*x2 + 0.59*x3 + 2.17*x4 >= 13)
m.addConstr(10*x0 - 5*x1 >= 0)
m.addConstr(1.35*x0 + 2.56*x3 <= 19)
m.addConstr(0.56*x1 + 2.69*x2 + 1.05*x4 <= 23)
m.addConstr(1.35*x0 + 2.56*x3 + 1.05*x4 <= 60)
m.addConstr(1.67*x1 + 2.17*x4 <= 59)
m.addConstr(1.67*x1 + 2.47*x2 <= 40)
m.addConstr(0.03*x0 + 1.67*x1 <= 161)
m.addConstr(0.59*x3 + 2.17*x4 <= 60)
m.addConstr(0.03*x0 + 0.59*x3 <= 127)
m.addConstr(0.03*x0 + 1.67*x1 + 2.17*x4 <= 57)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Strips of bacon: ", x0.varValue)
    print("Cornichons: ", x1.varValue)
    print("Slices of pizza: ", x2.varValue)
    print("Ham sandwiches: ", x3.varValue)
    print("Kiwis: ", x4.varValue)
else:
    print("The model is infeasible")
```

```json
{
    "sym_variables": [
        ["x0", "strips of bacon"],
        ["x1", "cornichons"],
        ["x2", "slices of pizza"],
        ["x3", "ham sandwiches"],
        ["x4", "kiwis"]
    ],
    "objective_function": "3*x0 + 7*x1 + 4*x2 + 5*x3 + 7*x4",
    "constraints": [
        "0.56*x1 + 2.69*x2 >= 16",
        "2.69*x2 + 2.56*x3 >= 14",
        "1.35*x0 + 0.56*x1 + 2.69*x2 + 2.56*x3 + 1.05*x4 >= 14",
        "0.03*x0 + 1.67*x1 >= 11",
        "0.03*x0 + 2.17*x4 >= 13",
        "0.03*x0 + 1.67*x1 + 2.47*x2 + 0.59*x3 + 2.17*x4 >= 13",
        "10*x0 - 5*x1 >= 0",
        "1.35*x0 + 2.56*x3 <= 19",
        "0.56*x1 + 2.69*x2 + 1.05*x4 <= 23",
        "1.35*x0 + 2.56*x3 + 1.05*x4 <= 60",
        "1.67*x1 + 2.17*x4 <= 59",
        "1.67*x1 + 2.47*x2 <= 40",
        "0.03*x0 + 1.67*x1 <= 161",
        "0.59*x3 + 2.17*x4 <= 60",
        "0.03*x0 + 0.59*x3 <= 127",
        "0.03*x0 + 1.67*x1 + 2.17*x4 <= 57"
    ]
}
```