## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- $x_1$ represents the milligrams of potassium
- $x_2$ represents the grams of protein
- $x_3$ represents the milligrams of vitamin D
- $x_4$ represents the milligrams of vitamin B12
- $x_5$ represents the milligrams of calcium

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $7.11x_1 + 6.69x_2 + 9.02x_3 + 1.68x_4 + 1.57x_5$.

## Step 3: List all the constraints in symbolic notation
Constraints:
1. $2x_1 \leq 182$
2. $5x_2 \leq 182$
3. $4x_3 \leq 182$
4. $4x_4 \leq 182$
5. $7x_5 \leq 182$
6. $2x_1 + 4x_3 \geq 23$
7. $2x_1 + 7x_5 \geq 35$
8. $5x_2 + 7x_5 \geq 12$
9. $2x_1 + 5x_2 \geq 21$
10. $4x_3 + 7x_5 \geq 28$
11. $4x_4 + 7x_5 \geq 16$
12. $2x_1 + 4x_4 \geq 18$
13. $4x_3 + 4x_4 \geq 25$
14. $2x_1 + 4x_3 + 4x_4 \geq 35$
15. $2x_1 + 5x_2 + 4x_4 \geq 35$
16. $4x_3 + 4x_4 + 7x_5 \geq 35$
17. $5x_2 + 4x_3 + 4x_4 \geq 35$
18. $2x_1 + 4x_3 + 7x_5 \geq 35$
19. $2x_1 + 4x_4 + 7x_5 \geq 35$
20. $2x_1 + 4x_3 + 4x_4 \geq 32$
21. $2x_1 + 5x_2 + 4x_4 \geq 32$
22. $4x_3 + 4x_4 + 7x_5 \geq 32$
23. $5x_2 + 4x_3 + 4x_4 \geq 32$
24. $2x_1 + 4x_3 + 7x_5 \geq 32$
25. $2x_1 + 4x_4 + 7x_5 \geq 32$
26. $2x_1 + 4x_3 + 4x_4 \geq 24$
27. $2x_1 + 5x_2 + 4x_4 \geq 24$
28. $4x_3 + 4x_4 + 7x_5 \geq 24$
29. $5x_2 + 4x_3 + 4x_4 \geq 24$
30. $2x_1 + 4x_3 + 7x_5 \geq 24$
31. $2x_1 + 4x_4 + 7x_5 \geq 24$
32. $2x_1 + 5x_2 + 4x_3 + 4x_4 + 7x_5 \geq 24$
33. $-2x_1 + 10x_4 \geq 0$
34. $4x_2 - 3x_3 \geq 0$
35. $2x_1 + 4x_3 \leq 72$
36. $5x_2 + 4x_4 \leq 79$
37. $4x_3 + 4x_4 \leq 124$
38. $2x_1 + 7x_5 \leq 78$
39. $5x_2 + 4x_3 \leq 130$
40. $2x_1 + 4x_4 \leq 140$

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x1', 'milligrams of potassium'), 
        ('x2', 'grams of protein'), 
        ('x3', 'milligrams of vitamin D'), 
        ('x4', 'milligrams of vitamin B12'), 
        ('x5', 'milligrams of calcium')
    ], 
    'objective_function': '7.11*x1 + 6.69*x2 + 9.02*x3 + 1.68*x4 + 1.57*x5', 
    'constraints': [
        '2*x1 <= 182', 
        '5*x2 <= 182', 
        '4*x3 <= 182', 
        '4*x4 <= 182', 
        '7*x5 <= 182', 
        '2*x1 + 4*x3 >= 23', 
        '2*x1 + 7*x5 >= 35', 
        '5*x2 + 7*x5 >= 12', 
        '2*x1 + 5*x2 >= 21', 
        '4*x3 + 7*x5 >= 28', 
        '4*x4 + 7*x5 >= 16', 
        '2*x1 + 4*x4 >= 18', 
        '4*x3 + 4*x4 >= 25', 
        '2*x1 + 4*x3 + 4*x4 >= 35', 
        '2*x1 + 5*x2 + 4*x4 >= 35', 
        '4*x3 + 4*x4 + 7*x5 >= 35', 
        '5*x2 + 4*x3 + 4*x4 >= 35', 
        '2*x1 + 4*x3 + 7*x5 >= 35', 
        '2*x1 + 4*x4 + 7*x5 >= 35', 
        '2*x1 + 4*x3 + 4*x4 >= 32', 
        '2*x1 + 5*x2 + 4*x4 >= 32', 
        '4*x3 + 4*x4 + 7*x5 >= 32', 
        '5*x2 + 4*x3 + 4*x4 >= 32', 
        '2*x1 + 4*x3 + 7*x5 >= 32', 
        '2*x1 + 4*x4 + 7*x5 >= 32', 
        '2*x1 + 4*x3 + 4*x4 >= 24', 
        '2*x1 + 5*x2 + 4*x4 >= 24', 
        '4*x3 + 4*x4 + 7*x5 >= 24', 
        '5*x2 + 4*x3 + 4*x4 >= 24', 
        '2*x1 + 4*x3 + 7*x5 >= 24', 
        '2*x1 + 4*x4 + 7*x5 >= 24', 
        '2*x1 + 5*x2 + 4*x3 + 4*x4 + 7*x5 >= 24', 
        '-2*x1 + 10*x4 >= 0', 
        '4*x2 - 3*x3 >= 0', 
        '2*x1 + 4*x3 <= 72', 
        '5*x2 + 4*x4 <= 79', 
        '4*x3 + 4*x4 <= 124', 
        '2*x1 + 7*x5 <= 78', 
        '5*x2 + 4*x3 <= 130', 
        '2*x1 + 4*x4 <= 140'
    ]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x1 = m.addVar(lb=-gp.GRB.INFINITY, name="milligrams of potassium")
x2 = m.addVar(lb=-gp.GRB.INFINITY, name="grams of protein")
x3 = m.addVar(lb=-gp.GRB.INFINITY, name="milligrams of vitamin D")
x4 = m.addVar(lb=-gp.GRB.INFINITY, name="milligrams of vitamin B12")
x5 = m.addVar(lb=-gp.GRB.INFINITY, name="milligrams of calcium")

# Objective function
m.setObjective(7.11*x1 + 6.69*x2 + 9.02*x3 + 1.68*x4 + 1.57*x5, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(2*x1 <= 182)
m.addConstr(5*x2 <= 182)
m.addConstr(4*x3 <= 182)
m.addConstr(4*x4 <= 182)
m.addConstr(7*x5 <= 182)

m.addConstr(2*x1 + 4*x3 >= 23)
m.addConstr(2*x1 + 7*x5 >= 35)
m.addConstr(5*x2 + 7*x5 >= 12)
m.addConstr(2*x1 + 5*x2 >= 21)
m.addConstr(4*x3 + 7*x5 >= 28)
m.addConstr(4*x4 + 7*x5 >= 16)
m.addConstr(2*x1 + 4*x4 >= 18)
m.addConstr(4*x3 + 4*x4 >= 25)
m.addConstr(2*x1 + 4*x3 + 4*x4 >= 35)
m.addConstr(2*x1 + 5*x2 + 4*x4 >= 35)
m.addConstr(4*x3 + 4*x4 + 7*x5 >= 35)
m.addConstr(5*x2 + 4*x3 + 4*x4 >= 35)
m.addConstr(2*x1 + 4*x3 + 7*x5 >= 35)
m.addConstr(2*x1 + 4*x4 + 7*x5 >= 35)

m.addConstr(2*x1 + 4*x3 + 4*x4 >= 32)
m.addConstr(2*x1 + 5*x2 + 4*x4 >= 32)
m.addConstr(4*x3 + 4*x4 + 7*x5 >= 32)
m.addConstr(5*x2 + 4*x3 + 4*x4 >= 32)
m.addConstr(2*x1 + 4*x3 + 7*x5 >= 32)
m.addConstr(2*x1 + 4*x4 + 7*x5 >= 32)

m.addConstr(2*x1 + 4*x3 + 4*x4 >= 24)
m.addConstr(2*x1 + 5*x2 + 4*x4 >= 24)
m.addConstr(4*x3 + 4*x4 + 7*x5 >= 24)
m.addConstr(5*x2 + 4*x3 + 4*x4 >= 24)
m.addConstr(2*x1 + 4*x3 + 7*x5 >= 24)
m.addConstr(2*x1 + 4*x4 + 7*x5 >= 24)

m.addConstr(2*x1 + 5*x2 + 4*x3 + 4*x4 + 7*x5 >= 24)

m.addConstr(-2*x1 + 10*x4 >= 0)
m.addConstr(4*x2 - 3*x3 >= 0)

m.addConstr(2*x1 + 4*x3 <= 72)
m.addConstr(5*x2 + 4*x4 <= 79)
m.addConstr(4*x3 + 4*x4 <= 124)
m.addConstr(2*x1 + 7*x5 <= 78)
m.addConstr(5*x2 + 4*x3 <= 130)
m.addConstr(2*x1 + 4*x4 <= 140)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Milligrams of potassium: ", x1.varValue)
    print("Grams of protein: ", x2.varValue)
    print("Milligrams of vitamin D: ", x3.varValue)
    print("Milligrams of vitamin B12: ", x4.varValue)
    print("Milligrams of calcium: ", x5.varValue)
    print("Objective function value: ", m.objVal)
else:
    print("No optimal solution found.")
```