To solve Julia's problem of minimizing her daily supplement cost while meeting the doctor's recommended intake of iron and biotin, we first need to establish a symbolic representation of the optimization problem. Let's denote:

- $x_1$ as the number of scoops of Gamma powder Julia should take.
- $x_2$ as the number of scoops of Delta powder Julia should take.

The objective function is to minimize the total cost, which can be represented as $1.5x_1 + 2.5x_2$, since each scoop of Gamma costs $1.5 and each scoop of Delta costs $2.5.

The constraints are:
1. Julia must consume at least 60 grams of iron: $7x_1 + 12x_2 \geq 60$.
2. Julia must consume at least 45 grams of biotin: $10x_1 + 9x_2 \geq 45$.
3. Non-negativity constraints, as Julia cannot take a negative number of scoops: $x_1 \geq 0$, $x_2 \geq 0$.

Therefore, the symbolic representation of the problem in JSON format is:
```json
{
    'sym_variables': [('x1', 'Number of scoops of Gamma'), ('x2', 'Number of scoops of Delta')],
    'objective_function': '1.5*x1 + 2.5*x2',
    'constraints': ['7*x1 + 12*x2 >= 60', '10*x1 + 9*x2 >= 45', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we will utilize the `gurobipy` library. First, ensure you have Gurobi installed and properly configured with a license.

Here is how you can implement and solve Julia's problem:
```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(name="Gamma_Scoops", lb=0, vtype=GRB.CONTINUOUS)
x2 = m.addVar(name="Delta_Scoops", lb=0, vtype=GRB.CONTINUOUS)

# Set the objective function: Minimize cost
m.setObjective(1.5*x1 + 2.5*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(7*x1 + 12*x2 >= 60, name="Iron_Requirement")
m.addConstr(10*x1 + 9*x2 >= 45, name="Biotin_Requirement")

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found. Gamma scoops: {x1.x}, Delta scoops: {x2.x}")
    print(f"Total cost: ${1.5*x1.x + 2.5*x2.x:.2f}")
else:
    print("No optimal solution found.")
```