To solve Joel's diet problem, we need to formulate it as a linear programming (LP) problem. Let's denote the number of chocolate protein shakes as $x_1$ and the number of vanilla meal replacement smoothies as $x_2$. 

The objective is to minimize the total cost, which can be represented by the objective function: 
\[ 8x_1 + 10x_2 \]

The constraints are:
- At least 150 units of protein: $35x_1 + 15x_2 \geq 150$
- At least 130 units of carbs: $20x_1 + 25x_2 \geq 130$
- No more than 50 units of fat: $3x_1 + 10x_2 \leq 50$

Here is the symbolic representation of the problem in JSON format:
```json
{
    'sym_variables': [('x1', 'number of chocolate protein shakes'), ('x2', 'number of vanilla meal replacement smoothies')],
    'objective_function': '8*x1 + 10*x2',
    'constraints': ['35*x1 + 15*x2 >= 150', '20*x1 + 25*x2 >= 130', '3*x1 + 10*x2 <= 50']
}
```

Now, let's implement this problem in Gurobi using Python:
```python
from gurobipy import *

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

# Create variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="chocolate_protein_shakes")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="vanilla_meal_replacement_smoothies")

# Set the objective function
m.setObjective(8*x1 + 10*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(35*x1 + 15*x2 >= 150, "protein_constraint")
m.addConstr(20*x1 + 25*x2 >= 130, "carbs_constraint")
m.addConstr(3*x1 + 10*x2 <= 50, "fat_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Chocolate protein shakes: {x1.x}")
    print(f"Vanilla meal replacement smoothies: {x2.x}")
    print(f"Total cost: {m.objVal}")
else:
    print("No optimal solution found")
```