## 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 symbolic variables as follows:
- $x_1$ represents the number of pianos.
- $x_2$ represents the number of guitars.

The objective is to maximize profit. Given that the profit per piano sold is $300 and the profit per guitar sold is $200, the objective function can be represented as:

Maximize: $300x_1 + 200x_2$

The constraints based on the given information are:
1. Space constraint: A piano takes 8 sq ft of space, a guitar takes 3 sq ft of space, and the store has 100 sq ft of space available.
   - $8x_1 + 3x_2 \leq 100$

2. Budget constraint: A piano costs the store $500 and a guitar costs the store $300, with a budget of $8000.
   - $500x_1 + 300x_2 \leq 8000$

3. Guitar percentage constraint: At least 30% of items in stock must be guitars.
   - $x_2 \geq 0.3(x_1 + x_2)$

4. Non-negativity constraint: The number of pianos and guitars cannot be negative.
   - $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'pianos'), ('x2', 'guitars')],
    'objective_function': '300*x1 + 200*x2',
    'constraints': [
        '8*x1 + 3*x2 <= 100',
        '500*x1 + 300*x2 <= 8000',
        'x2 >= 0.3*(x1 + x2)',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="pianos", vtype=gp.GRB.INTEGER, lb=0)  # Number of pianos
x2 = model.addVar(name="guitars", vtype=gp.GRB.INTEGER, lb=0)  # Number of guitars

# Objective function: Maximize profit
model.setObjective(300*x1 + 200*x2, gp.GRB.MAXIMIZE)

# Space constraint
model.addConstr(8*x1 + 3*x2 <= 100, name="space_constraint")

# Budget constraint
model.addConstr(500*x1 + 300*x2 <= 8000, name="budget_constraint")

# Guitar percentage constraint
model.addConstr(x2 >= 0.3*(x1 + x2), name="guitar_percentage_constraint")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal number of pianos: {x1.varValue}")
    print(f"Optimal number of guitars: {x2.varValue}")
    print(f"Maximum profit: {model.objVal}")
else:
    print("The model is infeasible.")
```