## Step 1: Define the symbolic variables
Let's define the symbolic variables for the objects in the problem:
- $x_1$ represents the number of hockey nets.
- $x_2$ represents the number of basketball hoops.

## Step 2: Translate the objective function into symbolic notation
The objective is to maximize profit. The profit per hockey net is $50, and the profit per basketball hoop is $75. Therefore, the objective function can be written as:
\[ \text{Maximize:} \quad 50x_1 + 75x_2 \]

## 3: Translate the constraints into symbolic notation
1. Space constraint: Each hockey net takes 5 sq ft, and each basketball hoop takes 3 sq ft. The warehouse has 300 sq ft available.
\[ 5x_1 + 3x_2 \leq 300 \]
2. Budget constraint: Each hockey net costs $100, and each basketball hoop costs $150. The warehouse has a budget of $10,000.
\[ 100x_1 + 150x_2 \leq 10000 \]
3. Hockey net proportion constraint: At least 65% of all items must be hockey nets.
\[ x_1 \geq 0.65(x_1 + x_2) \]
Simplifying:
\[ x_1 \geq 0.65x_1 + 0.65x_2 \]
\[ 0.35x_1 \geq 0.65x_2 \]
\[ x_1 - \frac{0.65}{0.35}x_2 \geq 0 \]
\[ x_1 - 1.8571x_2 \geq 0 \]
4. Non-negativity constraints:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

## 4: Provide the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'hockey nets'), ('x2', 'basketball hoops')],
'objective_function': '50*x1 + 75*x2',
'constraints': [
'5*x1 + 3*x2 <= 300',
'100*x1 + 150*x2 <= 10000',
'x1 - 1.8571*x2 >= 0',
'x1 >= 0',
'x2 >= 0'
]
}
```

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

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

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

    # Define the objective function
    model.setObjective(50*x1 + 75*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(5*x1 + 3*x2 <= 300, name="space_constraint")
    model.addConstr(100*x1 + 150*x2 <= 10000, name="budget_constraint")
    model.addConstr(x1 - 1.8571*x2 >= 0, name="hockey_net_proportion_constraint")

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```