## Step 1: Define the symbolic representation of the problem
The problem involves three variables: 'grams of fiber', 'milligrams of potassium', and 'milligrams of magnesium'. Let's denote these as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $5x_1 + x_2 + x_3$.

## Step 3: List all constraints in symbolic notation
1. $8.44x_1 \leq 242$
2. $6.43x_1 \leq 232$
3. $0.91x_1 \leq 177$
4. $0.9x_1 \leq 229$
5. $4.96x_1 \leq 102$
6. $8.9x_2 \leq 242$
7. $2.94x_2 \leq 232$
8. $4.62x_2 \leq 177$
9. $6.06x_2 \leq 229$
10. $7.58x_2 \leq 102$
11. $6.36x_3 \leq 242$
12. $3.65x_3 \leq 232$
13. $8.97x_3 \leq 177$
14. $8.69x_3 \leq 229$
15. $6.79x_3 \leq 102$
16. $8.44x_1 + 6.36x_3 \geq 69$
17. $8.9x_2 + 6.36x_3 \geq 37$
18. $8.44x_1 + 8.9x_2 + 6.36x_3 \geq 37$
19. $2.94x_2 + 3.65x_3 \geq 56$
20. $6.43x_1 + 2.94x_2 \geq 49$
21. $6.43x_1 + 2.94x_2 + 3.65x_3 \geq 49$
22. $0.91x_1 + 4.62x_2 \geq 33$
23. $0.91x_1 + 4.62x_2 + 8.97x_3 \geq 33$
24. $0.9x_1 + 6.06x_2 \geq 50$
25. $0.9x_1 + 8.69x_3 \geq 56$
26. $6.06x_2 + 8.69x_3 \geq 62$
27. $0.9x_1 + 6.06x_2 + 8.69x_3 \geq 62$
28. $4.96x_1 + 6.79x_3 \geq 17$
29. $4.96x_1 + 7.58x_2 + 6.79x_3 \geq 17$
30. $-2x_2 + 9x_3 \geq 0$
31. $-6x_1 + 3x_2 \geq 0$
32. $2.94x_2 + 3.65x_3 \leq 229$
33. $6.43x_1 + 2.94x_2 \leq 200$
34. $7.58x_2 + 6.79x_3 \leq 97$
35. $x_1 \in \mathbb{Z}$
36. $x_2 \in \mathbb{Z}$

## 4: Create the Gurobi model and variables
We will now create a Gurobi model and define the variables and constraints.

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

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

# Define the variables
x1 = m.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # grams of fiber
x2 = m.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # milligrams of potassium
x3 = m.addVar(name="x3")  # milligrams of magnesium

# Objective function: Minimize 5 * x1 + x2 + x3
m.setObjective(5 * x1 + x2 + x3, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(8.44 * x1 <= 242)
m.addConstr(6.43 * x1 <= 232)
m.addConstr(0.91 * x1 <= 177)
m.addConstr(0.9 * x1 <= 229)
m.addConstr(4.96 * x1 <= 102)

m.addConstr(8.9 * x2 <= 242)
m.addConstr(2.94 * x2 <= 232)
m.addConstr(4.62 * x2 <= 177)
m.addConstr(6.06 * x2 <= 229)
m.addConstr(7.58 * x2 <= 102)

m.addConstr(6.36 * x3 <= 242)
m.addConstr(3.65 * x3 <= 232)
m.addConstr(8.97 * x3 <= 177)
m.addConstr(8.69 * x3 <= 229)
m.addConstr(6.79 * x3 <= 102)

m.addConstr(8.44 * x1 + 6.36 * x3 >= 69)
m.addConstr(8.9 * x2 + 6.36 * x3 >= 37)
m.addConstr(8.44 * x1 + 8.9 * x2 + 6.36 * x3 >= 37)

m.addConstr(2.94 * x2 + 3.65 * x3 >= 56)
m.addConstr(6.43 * x1 + 2.94 * x2 >= 49)
m.addConstr(6.43 * x1 + 2.94 * x2 + 3.65 * x3 >= 49)

m.addConstr(0.91 * x1 + 4.62 * x2 >= 33)
m.addConstr(0.91 * x1 + 4.62 * x2 + 8.97 * x3 >= 33)

m.addConstr(0.9 * x1 + 6.06 * x2 >= 50)
m.addConstr(0.9 * x1 + 8.69 * x3 >= 56)
m.addConstr(6.06 * x2 + 8.69 * x3 >= 62)
m.addConstr(0.9 * x1 + 6.06 * x2 + 8.69 * x3 >= 62)

m.addConstr(4.96 * x1 + 6.79 * x3 >= 17)
m.addConstr(4.96 * x1 + 7.58 * x2 + 6.79 * x3 >= 17)

m.addConstr(-2 * x2 + 9 * x3 >= 0)
m.addConstr(-6 * x1 + 3 * x2 >= 0)

m.addConstr(2.94 * x2 + 3.65 * x3 <= 229)
m.addConstr(6.43 * x1 + 2.94 * x2 <= 200)
m.addConstr(7.58 * x2 + 6.79 * x3 <= 97)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
else:
    print("The model is infeasible")
```

## 6: Symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'grams of fiber'), ('x2', 'milligrams of potassium'), ('x3', 'milligrams of magnesium')],
    'objective_function': '5 * x1 + x2 + x3',
    'constraints': [
        '8.44 * x1 <= 242',
        '6.43 * x1 <= 232',
        '0.91 * x1 <= 177',
        '0.9 * x1 <= 229',
        '4.96 * x1 <= 102',
        '8.9 * x2 <= 242',
        '2.94 * x2 <= 232',
        '4.62 * x2 <= 177',
        '6.06 * x2 <= 229',
        '7.58 * x2 <= 102',
        '6.36 * x3 <= 242',
        '3.65 * x3 <= 232',
        '8.97 * x3 <= 177',
        '8.69 * x3 <= 229',
        '6.79 * x3 <= 102',
        '8.44 * x1 + 6.36 * x3 >= 69',
        '8.9 * x2 + 6.36 * x3 >= 37',
        '8.44 * x1 + 8.9 * x2 + 6.36 * x3 >= 37',
        '2.94 * x2 + 3.65 * x3 >= 56',
        '6.43 * x1 + 2.94 * x2 >= 49',
        '6.43 * x1 + 2.94 * x2 + 3.65 * x3 >= 49',
        '0.91 * x1 + 4.62 * x2 >= 33',
        '0.91 * x1 + 4.62 * x2 + 8.97 * x3 >= 33',
        '0.9 * x1 + 6.06 * x2 >= 50',
        '0.9 * x1 + 8.69 * x3 >= 56',
        '6.06 * x2 + 8.69 * x3 >= 62',
        '0.9 * x1 + 6.06 * x2 + 8.69 * x3 >= 62',
        '4.96 * x1 + 6.79 * x3 >= 17',
        '4.96 * x1 + 7.58 * x2 + 6.79 * x3 >= 17',
        '-2 * x2 + 9 * x3 >= 0',
        '-6 * x1 + 3 * x2 >= 0',
        '2.94 * x2 + 3.65 * x3 <= 229',
        '6.43 * x1 + 2.94 * x2 <= 200',
        '7.58 * x2 + 6.79 * x3 <= 97'
    ]
}
```