To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints using these variables.

Let's define:
- $x_1$ as the number of bookcases.
- $x_2$ as the number of dining tables.

The objective is to maximize profit, which can be represented by the objective function:
\[ \text{Maximize:} \quad 150x_1 + 200x_2 \]

Given constraints are:
1. Floor space constraint: $15x_1 + 8x_2 \leq 1200$
2. Bookcase ratio constraint: $x_1 \geq 0.20(x_1 + x_2)$
3. Capital constraint: $1200x_1 + 1500x_2 \leq 50000$
4. Non-negativity constraints: $x_1, x_2 \geq 0$

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of bookcases'), ('x2', 'number of dining tables')],
    'objective_function': '150*x1 + 200*x2',
    'constraints': [
        '15*x1 + 8*x2 <= 1200',
        'x1 >= 0.20*(x1 + x2)',
        '1200*x1 + 1500*x2 <= 50000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

Now, let's write the Gurobi code to solve this optimization problem:

```python
from gurobipy import *

# Create a new model
m = Model("Furniture_Store_Optimization")

# Define variables
x1 = m.addVar(name='bookcases', vtype=GRB.INTEGER)
x2 = m.addVar(name='dining_tables', vtype=GRB.INTEGER)

# Set objective function
m.setObjective(150*x1 + 200*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(15*x1 + 8*x2 <= 1200, name='floor_space')
m.addConstr(x1 >= 0.20*(x1 + x2), name='bookcase_ratio')
m.addConstr(1200*x1 + 1500*x2 <= 50000, name='capital')

# Optimize model
m.optimize()

# Print results
for v in m.getVars():
    print(f'{v.varName}: {v.x}')
print(f'Objective: {m.objVal}')
```