## Step 1: Define the symbolic variables
Let's define the symbolic variables for the objects in the problem:
- $x_1$ represents the number of bookcases
- $x_2$ represents the number of computer desks

## Step 2: Formulate the objective function
The profit per bookcase is $500 and the profit per computer desk is $80. The objective function to maximize profit is:
\[ \text{Maximize:} \quad 500x_1 + 80x_2 \]

## Step 3: Define the constraints
1. Space constraint: There are 1000 sq ft of space available. A bookcase requires 12 sq ft and a computer desk requires 5 sq ft.
\[ 12x_1 + 5x_2 \leq 1000 \]

2. Product mix constraint: At least 65% of all furniture must be computer desks.
\[ x_2 \geq 0.65(x_1 + x_2) \]
\[ 0.35x_2 \geq 0.65x_1 \]
\[ -0.65x_1 + 0.35x_2 \geq 0 \]

3. Capital constraint: A bookcase ties up $1200 and a computer desk ties up $200 in capital. The company wants a maximum of $22000 worth of capital tied up.
\[ 1200x_1 + 200x_2 \leq 22000 \]

4. Non-negativity constraints:
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

## 4: Symbolic Representation
The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'bookcase'), ('x2', 'computer desk')],
    'objective_function': '500*x1 + 80*x2',
    'constraints': [
        '12*x1 + 5*x2 <= 1000',
        '-0.65*x1 + 0.35*x2 >= 0',
        '1200*x1 + 200*x2 <= 22000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Gurobi Code
Now, let's implement this problem using Gurobi in Python:
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="bookcase", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="computer desk", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function
    model.setObjective(500 * x1 + 80 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(12 * x1 + 5 * x2 <= 1000, name="space_constraint")
    model.addConstr(-0.65 * x1 + 0.35 * x2 >= 0, name="product_mix_constraint")
    model.addConstr(1200 * x1 + 200 * x2 <= 22000, name="capital_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Bookcases: {x1.varValue}")
        print(f"Computer Desks: {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_furniture_problem()
```