To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, followed by the constraints.

### Symbolic Representation

- **Variables:**
  - \(x_1\): Number of mountain bikes
  - \(x_2\): Number of road bikes

- **Objective Function:**
  The objective is to maximize profit. Given that the mountain bike yields a profit of $300 and the road bike yields a profit of $500, the objective function can be represented as:
  \[ \text{Maximize:} \quad 300x_1 + 500x_2 \]

- **Constraints:**
  1. The total number of bikes should not exceed 150:
     \[ x_1 + x_2 \leq 150 \]
  2. The total value of bikes in stock should not exceed $40,000, with mountain bikes costing $750 and road bikes costing $1000:
     \[ 750x_1 + 1000x_2 \leq 40000 \]
  3. Non-negativity constraints, as the number of bikes cannot be negative:
     \[ x_1 \geq 0 \]
     \[ x_2 \geq 0 \]

### Solution in JSON Format

```json
{
  'sym_variables': [('x1', 'Number of mountain bikes'), ('x2', 'Number of road bikes')],
  'objective_function': '300*x1 + 500*x2',
  'constraints': ['x1 + x2 <= 150', '750*x1 + 1000*x2 <= 40000', 'x1 >= 0', 'x2 >= 0']
}
```

### Gurobi Code in Python

To solve this linear programming problem using Gurobi in Python, we'll use the following code:

```python
from gurobipy import *

# Create a model
m = Model("Bike_Shop_Problem")

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Mountain_Bikes")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Road_Bikes")

# Set objective function
m.setObjective(300*x1 + 500*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 150, "Total_Bikes_Constraint")
m.addConstr(750*x1 + 1000*x2 <= 40000, "Total_Value_Constraint")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Maximum Profit: {m.objVal}")
else:
    print("No optimal solution found")
```