## 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
- $x_1$ represents the number of packets of lemon candy.
- $x_2$ represents the number of packets of cherry candy.

### Objective Function
The objective is to maximize profit. Given that the profit per packet of lemon candy is $5 and the profit per packet of cherry candy is $7, the objective function can be written as:
\[ \text{Maximize:} \quad 5x_1 + 7x_2 \]

### Constraints
1. Time constraint: Each packet of lemon candy takes 20 minutes, and each packet of cherry candy takes 25 minutes. The store has 3000 minutes available.
\[ 20x_1 + 25x_2 \leq 3000 \]
2. Lemon candy packet limit: The store can make at most 100 lemon candy packets.
\[ x_1 \leq 100 \]
3. Cherry candy packet limit: The store can make at most 80 cherry candy packets.
\[ x_2 \leq 80 \]
4. Non-negativity constraint: The number of packets cannot be negative.
\[ x_1 \geq 0, x_2 \geq 0 \]

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'lemon candy packets'), ('x2', 'cherry candy packets')],
    'objective_function': 'Maximize: 5*x1 + 7*x2',
    'constraints': [
        '20*x1 + 25*x2 <= 3000',
        'x1 <= 100',
        'x2 <= 80',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="lemon_candy", lb=0, ub=100, vtype=gp.GRB.INTEGER)  # Number of lemon candy packets
x2 = model.addVar(name="cherry_candy", lb=0, ub=80, vtype=gp.GRB.INTEGER)  # Number of cherry candy packets

# Objective function: Maximize profit
model.setObjective(5 * x1 + 7 * x2, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(20 * x1 + 25 * x2 <= 3000, name="time_constraint")  # Time constraint
model.addConstr(x1 <= 100, name="lemon_limit")  # Lemon candy limit
model.addConstr(x2 <= 80, name="cherry_limit")  # Cherry candy limit

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: Lemon candy packets = {x1.varValue}, Cherry candy packets = {x2.varValue}")
    print(f"Maximum profit: ${5 * x1.varValue + 7 * x2.varValue}")
else:
    print("No optimal solution found.")
```