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

## Step 2: Translate the objective function into symbolic notation
The objective is to maximize profit. The profit per raft is $45, and the profit per kayak is $55. Therefore, the objective function can be written as:
\[ \text{Maximize:} \quad 45x_1 + 55x_2 \]

## 3: Translate the constraints into symbolic notation
1. Space constraint: Each raft takes 10 sq ft, and each kayak takes 12 sq ft. The warehouse has 400 sq ft available.
\[ 10x_1 + 12x_2 \leq 400 \]
2. Budget constraint: Each raft costs $200, and each kayak costs $250. The warehouse has a budget of $10,000.
\[ 200x_1 + 250x_2 \leq 10000 \]
3. Raft percentage constraint: At least 55% of all items must be rafts.
\[ x_1 \geq 0.55(x_1 + x_2) \]
\[ x_1 \geq 0.55x_1 + 0.55x_2 \]
\[ 0.45x_1 \geq 0.55x_2 \]
\[ 0.45x_1 - 0.55x_2 \geq 0 \]
4. Non-negativity constraints: The number of rafts and kayaks cannot be negative.
\[ x_1 \geq 0, x_2 \geq 0 \]

## 4: Symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'rafts'), ('x2', 'kayaks')],
'objective_function': '45*x1 + 55*x2',
'constraints': [
'10*x1 + 12*x2 <= 400',
'200*x1 + 250*x2 <= 10000',
'0.45*x1 - 0.55*x2 >= 0',
'x1 >= 0',
'x2 >= 0'
]
}
```

## 5: Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="rafts", lb=0, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="kayaks", lb=0, vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(45 * x1 + 55 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(10 * x1 + 12 * x2 <= 400, name="space_constraint")
    model.addConstr(200 * x1 + 250 * x2 <= 10000, name="budget_constraint")
    model.addConstr(0.45 * x1 - 0.55 * x2 >= 0, name="raft_percentage_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of rafts: {x1.varValue}")
        print(f"Number of kayaks: {x2.varValue}")
        print(f"Maximum profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```