To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's define:
- $x_1$ as the number of packets of lemon candy to make.
- $x_2$ as the number of packets of cherry candy to make.

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

The constraints are based on the time available and the maximum number of packets that can be made for each type of candy:
1. Time constraint: Making lemon candies takes 20 minutes per packet, and making cherry candies takes 25 minutes per packet. The total time available is 3000 minutes.
\[ 20x_1 + 25x_2 \leq 3000 \]
2. Maximum packets of lemon candy: At most 100 packets can be made.
\[ x_1 \leq 100 \]
3. Maximum packets of cherry candy: At most 80 packets can be made.
\[ x_2 \leq 80 \]
4. Non-negativity constraint: The number of packets cannot be negative.
\[ x_1, x_2 \geq 0 \]

Thus, the symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'number of packets of lemon candy'), ('x2', 'number of packets of cherry candy')],
    'objective_function': '5*x1 + 7*x2',
    'constraints': [
        '20*x1 + 25*x2 <= 3000',
        'x1 <= 100',
        'x2 <= 80',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

To solve this problem using Gurobi in Python, we can use the following code:

```python
from gurobipy import *

# Create a model
m = Model("Candy Optimization")

# Define variables
x1 = m.addVar(lb=0, name="lemon_candy_packets")
x2 = m.addVar(lb=0, name="cherry_candy_packets")

# Set the objective function
m.setObjective(5*x1 + 7*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(20*x1 + 25*x2 <= 3000, "time_constraint")
m.addConstr(x1 <= 100, "max_lemon_candy")
m.addConstr(x2 <= 80, "max_cherry_candy")

# Optimize the model
m.optimize()

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