## Problem Description and Symbolic Representation

The problem involves maximizing profit by determining the optimal number of scooters and bikes to produce given certain constraints on machine usage.

### Symbolic Representation

Let's denote:
- \(x_1\) as the number of scooters produced
- \(x_2\) as the number of bikes produced

The objective function to maximize profit is: \(100x_1 + 50x_2\)

Constraints:
1. Grinder usage: \(2x_1 + 4x_2 \leq 10\)
2. Polisher usage: \(3x_1 + 3x_2 \leq 10\)
3. Non-negativity: \(x_1 \geq 0, x_2 \geq 0\)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'scooters'), ('x2', 'bikes')],
    'objective_function': '100*x1 + 50*x2',
    'constraints': [
        '2*x1 + 4*x2 <= 10',
        '3*x1 + 3*x2 <= 10',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Scooters_and_Bikes")

# Define variables
x1 = model.addVar(name="scooters", lb=0, vtype=gp.GRB.CONTINUOUS)
x2 = model.addVar(name="bikes", lb=0, vtype=gp.GRB.CONTINUOUS)

# Objective function: maximize profit
model.setObjective(100*x1 + 50*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(2*x1 + 4*x2 <= 10, name="grinder_constraint")
model.addConstr(3*x1 + 3*x2 <= 10, name="polisher_constraint")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: {model.getVarByName('scooters').varName} = {model.getVarByName('scooters').x}, {model.getVarByName('bikes').varName} = {model.getVarByName('bikes').x}")
    print(f"Maximum profit: ${model.objVal:.2f}")
else:
    print("No optimal solution found.")
```