## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- $x_0$ : lemons
- $x_1$ : peanutbutter sandwiches
- $x_2$ : hamburgers
- $x_3$ : slices of pizza

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is: $6.6x_0 + 7.81x_1 + 2.96x_2 + 9.02x_3$

## Step 3: List all constraints in symbolic notation
Constraints:
1. $14x_0 + 30x_1 + 9x_2 + 19x_3 \leq 696$ (iron)
2. $30x_0 + 19x_1 + 9x_2 + 11x_3 \leq 295$ (umami index)
3. $30x_1 + 9x_2 \geq 141$ (iron from peanutbutter sandwiches and hamburgers)
4. $14x_0 + 9x_2 \geq 102$ (iron from lemons and hamburgers)
5. $14x_0 + 19x_3 \geq 64$ (iron from lemons and slices of pizza)
6. $14x_0 + 9x_2 + 19x_3 \geq 122$ (iron from lemons, hamburgers, and slices of pizza)
7. $30x_1 + 9x_2 + 19x_3 \geq 122$ (iron from peanutbutter sandwiches, hamburgers, and slices of pizza)
8. $14x_0 + 9x_2 + 19x_3 \geq 166$ (iron from lemons, hamburgers, and slices of pizza)
9. $30x_1 + 9x_2 + 19x_3 \geq 166$ (iron from peanutbutter sandwiches, hamburgers, and slices of pizza)
10. $30x_0 + 19x_1 + 9x_2 \geq 65$ (umami from lemons, peanutbutter sandwiches, and hamburgers)
11. $30x_0 + 9x_2 + 11x_3 \geq 65$ (umami from lemons, hamburgers, and slices of pizza)
12. $30x_0 + 19x_1 + 11x_3 \geq 65$ (umami from lemons, peanutbutter sandwiches, and slices of pizza)
13. $30x_0 + 19x_1 + 9x_2 \geq 54$ (umami from lemons, peanutbutter sandwiches, and hamburgers)
14. $30x_0 + 9x_2 + 11x_3 \geq 54$ (umami from lemons, hamburgers, and slices of pizza)
15. $30x_0 + 19x_1 + 11x_3 \geq 54$ (umami from lemons, peanutbutter sandwiches, and slices of pizza)
16. $30x_0 + 19x_1 + 9x_2 \geq 42$ (umami from lemons, peanutbutter sandwiches, and hamburgers)
17. $30x_0 + 9x_2 + 11x_3 \geq 42$ (umami from lemons, hamburgers, and slices of pizza)
18. $30x_0 + 19x_1 + 11x_3 \geq 42$ (umami from lemons, peanutbutter sandwiches, and slices of pizza)
19. $14x_0 + 9x_2 \leq 217$ (iron from lemons and hamburgers)
20. $14x_0 + 30x_1 \leq 401$ (iron from lemons and peanutbutter sandwiches)
21. $30x_1 + 9x_2 \leq 623$ (iron from peanutbutter sandwiches and hamburgers)
22. $14x_0 + 30x_1 + 9x_2 + 19x_3 \leq 623$ (iron from all sources)
23. $30x_0 + 19x_1 \leq 214$ (umami from lemons and peanutbutter sandwiches)
24. $19x_1 + 11x_3 \leq 109$ (umami from peanutbutter sandwiches and slices of pizza)
25. $30x_0 + 19x_1 + 11x_3 \leq 94$ (umami from lemons, peanutbutter sandwiches, and slices of pizza)
26. $30x_0 + 19x_1 + 9x_2 + 11x_3 \leq 94$ (umami from all sources)

## Step 4: Define variable types
- $x_0$ (lemons): integer
- $x_1$ (peanutbutter sandwiches): integer
- $x_2$ (hamburgers): continuous
- $x_3$ (slices of pizza): integer

## 5: Formulate the problem in Gurobi

```python
import gurobi

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

# Define variables
x0 = m.addVar(name="lemons", vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name="peanutbutter sandwiches", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="hamburgers", vtype=gurobi.GRB.CONTINUOUS)
x3 = m.addVar(name="slices of pizza", vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(6.6 * x0 + 7.81 * x1 + 2.96 * x2 + 9.02 * x3, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(14 * x0 + 30 * x1 + 9 * x2 + 19 * x3 <= 696)
m.addConstr(30 * x0 + 19 * x1 + 9 * x2 + 11 * x3 <= 295)
m.addConstr(30 * x1 + 9 * x2 >= 141)
m.addConstr(14 * x0 + 9 * x2 >= 102)
m.addConstr(14 * x0 + 19 * x3 >= 64)
m.addConstr(14 * x0 + 9 * x2 + 19 * x3 >= 122)
m.addConstr(30 * x1 + 9 * x2 + 19 * x3 >= 122)
m.addConstr(14 * x0 + 9 * x2 + 19 * x3 >= 166)
m.addConstr(30 * x1 + 9 * x2 + 19 * x3 >= 166)
m.addConstr(30 * x0 + 19 * x1 + 9 * x2 >= 65)
m.addConstr(30 * x0 + 9 * x2 + 11 * x3 >= 65)
m.addConstr(30 * x0 + 19 * x1 + 11 * x3 >= 65)
m.addConstr(30 * x0 + 19 * x1 + 9 * x2 >= 54)
m.addConstr(30 * x0 + 9 * x2 + 11 * x3 >= 54)
m.addConstr(30 * x0 + 19 * x1 + 11 * x3 >= 54)
m.addConstr(30 * x0 + 19 * x1 + 9 * x2 >= 42)
m.addConstr(30 * x0 + 9 * x2 + 11 * x3 >= 42)
m.addConstr(30 * x0 + 19 * x1 + 11 * x3 >= 42)
m.addConstr(14 * x0 + 9 * x2 <= 217)
m.addConstr(14 * x0 + 30 * x1 <= 401)
m.addConstr(30 * x1 + 9 * x2 <= 623)
m.addConstr(14 * x0 + 30 * x1 + 9 * x2 + 19 * x3 <= 623)
m.addConstr(30 * x0 + 19 * x1 <= 214)
m.addConstr(19 * x1 + 11 * x3 <= 109)
m.addConstr(30 * x0 + 19 * x1 + 11 * x3 <= 94)
m.addConstr(30 * x0 + 19 * x1 + 9 * x2 + 11 * x3 <= 94)

# Solve the model
m.optimize()

# Print the solution
print("Objective: ", m.objVal)
print("lemons: ", x0.varValue)
print("peanutbutter sandwiches: ", x1.varValue)
print("hamburgers: ", x2.varValue)
print("slices of pizza: ", x3.varValue)
```

### Symbolic Representation

```json
{
    "sym_variables": [
        ["x0", "lemons"],
        ["x1", "peanutbutter sandwiches"],
        ["x2", "hamburgers"],
        ["x3", "slices of pizza"]
    ],
    "objective_function": "6.6x0 + 7.81x1 + 2.96x2 + 9.02x3",
    "constraints": [
        "14x0 + 30x1 + 9x2 + 19x3 <= 696",
        "30x0 + 19x1 + 9x2 + 11x3 <= 295",
        "30x1 + 9x2 >= 141",
        "14x0 + 9x2 >= 102",
        "14x0 + 19x3 >= 64",
        "14x0 + 9x2 + 19x3 >= 122",
        "30x1 + 9x2 + 19x3 >= 122",
        "14x0 + 9x2 + 19x3 >= 166",
        "30x1 + 9x2 + 19x3 >= 166",
        "30x0 + 19x1 + 9x2 >= 65",
        "30x0 + 9x2 + 11x3 >= 65",
        "30x0 + 19x1 + 11x3 >= 65",
        "30x0 + 19x1 + 9x2 >= 54",
        "30x0 + 9x2 + 11x3 >= 54",
        "30x0 + 19x1 + 11x3 >= 54",
        "30x0 + 19x1 + 9x2 >= 42",
        "30x0 + 9x2 + 11x3 >= 42",
        "30x0 + 19x1 + 11x3 >= 42",
        "14x0 + 9x2 <= 217",
        "14x0 + 30x1 <= 401",
        "30x1 + 9x2 <= 623",
        "14x0 + 30x1 + 9x2 + 19x3 <= 623",
        "30x0 + 19x1 <= 214",
        "19x1 + 11x3 <= 109",
        "30x0 + 19x1 + 11x3 <= 94",
        "30x0 + 19x1 + 9x2 + 11x3 <= 94"
    ]
}
```