## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, and list the constraints.

### Variables
- $x_1$: Number of apple pies
- $x_2$: Number of peach pies

### Objective Function
The objective is to maximize profit. Given that the profit per apple pie is $7 and per peach pie is $8, the objective function can be represented as:
\[ \text{Maximize:} \quad 7x_1 + 8x_2 \]

### Constraints
1. Sell at least 15 apple pies: $x_1 \geq 15$
2. Sell at least 12 peach pies: $x_2 \geq 12$
3. Can make at most 20 apple pies: $x_1 \leq 20$
4. Can make at most 18 peach pies: $x_2 \leq 18$
5. Total pies (either type) cannot exceed 30: $x_1 + x_2 \leq 30$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'apple pies'), ('x2', 'peach pies')],
    'objective_function': '7*x1 + 8*x2',
    'constraints': [
        'x1 >= 15',
        'x2 >= 12',
        'x1 <= 20',
        'x2 <= 18',
        'x1 + x2 <= 30'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("PieShop")

# Define variables
x1 = model.addVar(lb=0, ub=gp.GRB.INFINITY, name="apple_pies")
x2 = model.addVar(lb=0, ub=gp.GRB.INFINITY, name="peach_pies")

# Set bounds according to the problem
x1.lb = 15
x2.lb = 12
x1.ub = 20
x2.ub = 18

# Objective function
model.setObjective(7*x1 + 8*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 <= 20, name="apple_pies_max")
model.addConstr(x2 <= 18, name="peach_pies_max")
model.addConstr(x1 + x2 <= 30, name="total_pies_max")

# Add constraints that are already considered in bounds
# model.addConstr(x1 >= 15, name="apple_pies_min")
# model.addConstr(x2 >= 12, name="peach_pies_min")

# Solve the model
model.optimize()

# Print solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal solution:")
    print(f"Apple pies: {x1.varValue}")
    print(f"Peach pies: {x2.varValue}")
    print(f"Max Profit: {model.objVal}")
else:
    print("No optimal solution found")
```