## Step 1: Define the optimization problem
The problem is to minimize the objective function: $7 \cdot (milligrams\ of\ vitamin\ K) \cdot (grams\ of\ fiber) + 8 \cdot (grams\ of\ fiber)$, subject to various constraints.

## Step 2: Identify the variables and their attributes
Let $x_0$ be the milligrams of vitamin K and $x_1$ be the grams of fiber. The attributes or resources are given as:
- $r_0$: cognitive performance index
- $r_1$: muscle growth index
- $r_2$: digestive support index
- $r_3$: immune support index

With specific values:
- $r_0$: $x_0 = 10$, $x_1 = 14$, $upper\_bound = 42$
- $r_1$: $x_0 = 5$, $x_1 = 15$, $upper\_bound = 34$
- $r_2$: $x_0 = 7$, $x_1 = 2$, $upper\_bound = 99$
- $r_3$: $x_0 = 17$, $x_1 = 8$, $upper\_bound = 42$

## 3: Formulate the objective function
The objective function to minimize is: $7x_0x_1 + 8x_1$.

## 4: Formulate the constraints
1. $10x_0 + 14x_1 \geq 12$
2. $5x_0 + 15x_1 \geq 16$
3. $7x_0^2 + 2x_1^2 \geq 30$
4. $17x_0^2 + 8x_1^2 \geq 18$
5. $-3x_0 + 5x_1 \geq 0$
6. $10x_0^2 + 14x_1^2 \leq 31$
7. $5x_0 + 15x_1 \leq 19$
8. $7x_0^2 + 2x_1^2 \leq 76$
9. $17x_0 + 8x_1 \leq 41$

## 5: Write the Gurobi code
```python
import gurobi

def optimize_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x0 = model.addVar(name="milligrams_of_vitamin_K", lb=0)  # Assuming non-negative
    x1 = model.addVar(name="grams_of_fiber", lb=0)  # Assuming non-negative

    # Objective function
    model.setObjective(7 * x0 * x1 + 8 * x1, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(10 * x0 + 14 * x1 >= 12, name="cognitive_performance")
    model.addConstr(5 * x0 + 15 * x1 >= 16, name="muscle_growth")
    model.addConstr(7 * x0**2 + 2 * x1**2 >= 30, name="digestive_support")
    model.addConstr(17 * x0**2 + 8 * x1**2 >= 18, name="immune_support")
    model.addConstr(-3 * x0 + 5 * x1 >= 0, name="linear_constraint")
    model.addConstr(10 * x0**2 + 14 * x1**2 <= 31, name="cognitive_performance_squared")
    model.addConstr(5 * x0 + 15 * x1 <= 19, name="muscle_growth_squared")
    model.addConstr(7 * x0**2 + 2 * x1**2 <= 76, name="digestive_support_squared")
    model.addConstr(17 * x0 + 8 * x1 <= 41, name="immune_support_linear")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin K: {x0.varValue}")
        print(f"Grams of fiber: {x1.varValue}")
        print(f"Objective function value: {model.objVal}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

optimize_problem()
```