To solve the given problem, we first need to translate the natural language description into a symbolic representation. Let's define:

- $x_1$ as the number of blue pills purchased
- $x_2$ as the number of red pills purchased

The objective is to minimize the total cost, which can be represented as:
\[ \text{Minimize} \quad 1x_1 + 2x_2 \]

Given the requirements:
- At least 100 units of blood pressure medication: $10x_1 + 5x_2 \geq 100$
- At least 70 units of diabetes medication: $3x_1 + 7x_2 \geq 70$

Also, since we cannot purchase a negative number of pills, we have:
- $x_1 \geq 0$
- $x_2 \geq 0$

The symbolic representation in JSON format is:

```json
{
    'sym_variables': [('x1', 'number of blue pills'), ('x2', 'number of red pills')],
    'objective_function': '1*x1 + 2*x2',
    'constraints': ['10*x1 + 5*x2 >= 100', '3*x1 + 7*x2 >= 70', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem in Gurobi using Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.INTEGER, name="blue_pills")
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="red_pills")

# Set the objective function
m.setObjective(1*x1 + 2*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(10*x1 + 5*x2 >= 100, "blood_pressure")
m.addConstr(3*x1 + 7*x2 >= 70, "diabetes")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Blue pills: {x1.x}")
    print(f"Red pills: {x2.x}")
    print(f"Total cost: ${1*x1.x + 2*x2.x:.2f}")
else:
    print("No optimal solution found")
```