To solve the optimization problem described, we will use Gurobi, a powerful solver for linear and mixed-integer programming problems. The problem involves minimizing an objective function subject to several constraints involving milligrams of calcium and potassium.

First, let's identify the variables and constraints:

- Variables:
  - `x0`: milligrams of calcium
  - `x1`: milligrams of potassium

- Objective Function: Minimize `7*x0 + 5*x1`

- Constraints based on the provided information:
  1. Kidney support index for calcium: `8*x0`
  2. Energy stability index for calcium: `1*x0`
  3. Digestive support index for calcium: `4*x0`
  4. Cognitive performance index for calcium: `12*x0`
  5. Kidney support index for potassium: `4*x1`
  6. Energy stability index for potassium: `7*x1`
  7. Digestive support index for potassium: `4*x1`
  8. Cognitive performance index for potassium: `7*x1`

- Combined constraints:
  - Total kidney support index ≥ 18
  - Total energy stability index ≥ 31
  - Total digestive support index ≥ 36
  - Total cognitive performance index ≥ 26
  - Additional linear constraint: `x0 - 6*x1 ≥ 0`
  
- Upper bound constraints on combined indices:
  - Kidney support ≤ 97
  - Energy stability ≤ 120
  - Digestive support ≤ 62
  - Cognitive performance ≤ 102

Given the complexity and the specific requirements of the problem, including the need for whole numbers of milligrams of potassium but allowing non-whole numbers of milligrams of calcium, we'll implement this in Gurobi using Python.

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_calcium")
x1 = m.addVar(vtype=GRB.INTEGER, name="milligrams_of_potassium")  # Whole numbers

# Objective function: Minimize 7*x0 + 5*x1
m.setObjective(7*x0 + 5*x1, GRB.MINIMIZE)

# Constraints
m.addConstr(8*x0 + 4*x1 >= 18, name="kidney_support_index_min")
m.addConstr(8*x0 + 4*x1 <= 97, name="kidney_support_index_max")

m.addConstr(x0 + 7*x1 >= 31, name="energy_stability_index_min")
m.addConstr(x0 + 7*x1 <= 120, name="energy_stability_index_max")

m.addConstr(4*x0 + 4*x1 >= 36, name="digestive_support_index_min")
m.addConstr(4*x0 + 4*x1 <= 62, name="digestive_support_index_max")

m.addConstr(12*x0 + 7*x1 >= 26, name="cognitive_performance_index_min")
m.addConstr(12*x0 + 7*x1 <= 102, name="cognitive_performance_index_max")

m.addConstr(x0 - 6*x1 >= 0, name="additional_linear_constraint")

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of Calcium: {x0.x}")
    print(f"Milligrams of Potassium: {int(x1.x)}")  # Cast to int for clarity
else:
    print("No optimal solution found")
```
```python
```