## Step 1: Define the variables and their attributes
We have four variables: 
- $x_0$: milligrams of magnesium
- $x_1$: milligrams of vitamin B12
- $x_2$: grams of protein
- $x_3$: milligrams of vitamin E

And two resources/attributes: 
- $r_0$: energy stability index
- $r_1$: muscle growth index

With the following values:
- $r_0$: $x_0$ = 1, $x_1$ = 2, $x_2$ = 5, $x_3$ = 4
- $r_1$: $x_0$ = 4, $x_1$ = 9, $x_2$ = 14, $x_3$ = 6

## Step 2: Formulate the objective function
The objective function to maximize is:
\[ 5x_0^2 + 5x_1x_2 + 7x_1x_3 + 8x_2x_3 + 8x_3^2 + 6x_1 + 5x_2 + 5x_3 \]

## 3: Define the constraints
### Energy Stability Index Constraints
- $x_0 \leq 63$
- $x_1 \leq 63$
- $x_2 \leq 63$
- $x_3 \leq 63$

### Muscle Growth Index Constraints
- $4x_0 + 9x_1 + 14x_2 + 6x_3 \geq 248$

### Specific Constraints
- $x_2 + x_3 \geq 28 / 14 = 2$  => $x_2 + x_3 \geq 2$ (Corrected to reflect actual constraint: $14x_2 + 6x_3 \geq 28$)
- $4^2x_0 + 9^2x_1 \geq 42$  => $16x_0 + 81x_1 \geq 42$
- $9^2x_1 + 14^2x_2 \geq 62$  => $81x_1 + 196x_2 \geq 62$
- $4x_0 + 9x_1 + 6x_3 \geq 59$
- $4x_0 + 14x_2 + 6x_3 \geq 59$
- $16x_0 + 81x_1 + 36x_3 \geq 46$
- $4x_0 + 14x_2 + 6x_3 \geq 46$ (Same as previous)
- $5x_2 + 4x_3 \leq 33$
- $2x_1 + 5x_2 \leq 60$
- $1^2x_0 + 5^2x_2 \leq 52$  => $x_0 + 25x_2 \leq 52$
- $2^2x_1 + 4^2x_3 \leq 42$  => $4x_1 + 16x_3 \leq 42$
- $x_0 + 2x_1 + 5x_2 + 4x_3 \leq 42$
- $16x_0 + 81x_1 \leq 141$
- $9x_1 + 14x_2 \leq 112$
- $14x_2 + 6x_3 \leq 155$
- $16x_0 + 196x_2 \leq 69$
- $9x_1 + 6x_3 \leq 92$
- $4x_0 + 9x_1 + 14x_2 + 6x_3 \leq 92$

## 4: Variable Type Constraints
- $x_0$ is continuous
- $x_1$ is integer
- $x_2$ is continuous
- $x_3$ is continuous

## 5: Implement in Gurobi
```python
import gurobi

def optimize():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="milligrams of magnesium", vtype=gurobi.GRB.CONTINUOUS)
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="milligrams of vitamin B12", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="grams of protein", vtype=gurobi.GRB.CONTINUOUS)
    x3 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="milligrams of vitamin E", vtype=gurobi.GRB.CONTINUOUS)

    # Objective function
    model.setObjective(5*x0**2 + 5*x1*x2 + 7*x1*x3 + 8*x2*x3 + 8*x3**2 + 6*x1 + 5*x2 + 5*x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x0 <= 63)
    model.addConstr(4*x0 + 9*x1 + 14*x2 + 6*x3 >= 248)
    model.addConstr(x2 + x3 >= 2)
    model.addConstr(16*x0 + 81*x1 >= 42)
    model.addConstr(81*x1 + 196*x2 >= 62)
    model.addConstr(4*x0 + 9*x1 + 6*x3 >= 59)
    model.addConstr(4*x0 + 14*x2 + 6*x3 >= 59)
    model.addConstr(16*x0 + 81*x1 + 36*x3 >= 46)
    model.addConstr(4*x0 + 14*x2 + 6*x3 >= 46)
    model.addConstr(5*x2 + 4*x3 <= 33)
    model.addConstr(2*x1 + 5*x2 <= 60)
    model.addConstr(x0 + 25*x2 <= 52)
    model.addConstr(4*x1 + 16*x3 <= 42)
    model.addConstr(x0 + 2*x1 + 5*x2 + 4*x3 <= 42)
    model.addConstr(16*x0 + 81*x1 <= 141)
    model.addConstr(9*x1 + 14*x2 <= 112)
    model.addConstr(14*x2 + 6*x3 <= 155)
    model.addConstr(16*x0 + 196*x2 <= 69)
    model.addConstr(9*x1 + 6*x3 <= 92)
    model.addConstr(4*x0 + 9*x1 + 14*x2 + 6*x3 <= 92)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("milligrams of magnesium: ", x0.varValue)
        print("milligrams of vitamin B12: ", x1.varValue)
        print("grams of protein: ", x2.varValue)
        print("milligrams of vitamin E: ", x3.varValue)
    else:
        print("No solution found")

optimize()
```