## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The goal is to minimize the cost of purchasing pills while meeting the patient's requirements for blood pressure and diabetes medication.

Let's define the decision variables:

* `x`: the number of blue pills to purchase
* `y`: the number of red pills to purchase

The objective function is to minimize the total cost:

* `Cost = 1x + 2y`

The patient requires at least 100 units of blood pressure medication and 70 units of diabetes medication per week. The constraints are:

* `10x + 5y >= 100` (blood pressure medication requirement)
* `3x + 7y >= 70` (diabetes medication requirement)

Additionally, `x` and `y` must be non-negative integers, as they represent the number of pills to purchase:

* `x >= 0`
* `y >= 0`

## Gurobi Code

```python
import gurobi

# Create a new Gurobi model
model = gurobi.Model()

# Define the decision variables
x = model.addVar(lb=0, name="blue_pills")
y = model.addVar(lb=0, name="red_pills")

# Define the objective function
model.setObjective(x + 2 * y, gurobi.GRB.MINIMIZE)

# Define the constraints
model.addConstr(10 * x + 5 * y >= 100, name="blood_pressure_requirement")
model.addConstr(3 * x + 7 * y >= 70, name="diabetes_requirement")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Blue pills: {x.varValue}")
    print(f"Red pills: {y.varValue}")
    print(f"Total cost: {model.objVal}")
else:
    print("No optimal solution found.")
```

This code defines a Gurobi model, adds the decision variables and constraints, sets the objective function, and optimizes the model. If an optimal solution is found, it prints the number of blue and red pills to purchase and the total cost. Otherwise, it indicates that no optimal solution was found.