## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of fridges
- $x_2$ represents the number of stoves

## Step 2: Formulate the objective function
The profit per fridge is $400 and the profit per stove is $500. The objective is to maximize the total profit:
\[ \text{Maximize:} \quad 400x_1 + 500x_2 \]

## Step 3: Define the constraints
1. **Floor Space Constraint:** The store has 1000 sq ft of floor space available. A fridge requires 10 sq ft and a stove requires 15 sq ft.
\[ 10x_1 + 15x_2 \leq 1000 \]

2. **Product Mix Constraint:** At least 40% of all appliances in stock must be fridges.
\[ x_1 \geq 0.4(x_1 + x_2) \]
\[ 0.6x_1 \geq 0.4x_2 \]
\[ 0.6x_1 - 0.4x_2 \geq 0 \]
\[ 3x_1 - 2x_2 \geq 0 \]

3. **Capital Constraint:** The store wants to have a maximum of $40,000 worth of capital tied up. A fridge ties up $1000 and a stove ties up $1200.
\[ 1000x_1 + 1200x_2 \leq 40000 \]

4. **Non-Negativity Constraints:** The number of fridges and stoves cannot be negative.
\[ x_1 \geq 0, x_2 \geq 0 \]

## Step 4: Symbolic Representation
```json
{
'sym_variables': [('x1', 'fridge'), ('x2', 'stove')],
'objective_function': '400*x1 + 500*x2',
'constraints': [
    '10*x1 + 15*x2 <= 1000',
    '3*x1 - 2*x2 >= 0',
    '1000*x1 + 1200*x2 <= 40000',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## Step 5: Gurobi Code
```python
import gurobi

def solve_appliance_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name="fridge", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="stove", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function
    model.setObjective(400*x1 + 500*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(10*x1 + 15*x2 <= 1000, name="floor_space")
    model.addConstr(3*x1 - 2*x2 >= 0, name="product_mix")
    model.addConstr(1000*x1 + 1200*x2 <= 40000, name="capital")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Fridges: {x1.varValue}")
        print(f"Stoves: {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("The model is infeasible")

solve_appliance_problem()
```