To solve this problem, we first need to define the decision variables and the objective function. Let's denote the number of blue pills as `B` and the number of red pills as `R`. The objective is to minimize the total cost, which can be calculated as `1*B + 2*R`, since each blue pill costs $1 and each red pill costs $2.

The constraints are:
- The patient requires at least 100 units of blood pressure medication. Given that each blue pill contains 10 units and each red pill contains 5 units of blood pressure medication, we can express this constraint as `10*B + 5*R >= 100`.
- The patient requires at least 70 units of diabetes medication. With each blue pill containing 3 units and each red pill containing 7 units of diabetes medication, this constraint is `3*B + 7*R >= 70`.

We also know that the patient cannot buy a negative number of pills, so both `B` and `R` must be non-negative.

Here's how we can translate these constraints into Gurobi code in Python:

```python
from gurobipy import *

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

# Define the decision variables
B = m.addVar(vtype=GRB.INTEGER, name="Blue_Pills", lb=0)
R = m.addVar(vtype=GRB.INTEGER, name="Red_Pills", lb=0)

# Set the objective function: minimize the total cost
m.setObjective(1*B + 2*R, GRB.MINIMIZE)

# Add constraints
m.addConstr(10*B + 5*R >= 100, "Blood_Pressure_Requirement")
m.addConstr(3*B + 7*R >= 70, "Diabetes_Requirement")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: Buy {int(B.x)} blue pills and {int(R.x)} red pills.")
else:
    print("No optimal solution found.")

```