## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'potatoes', 'tomatoes', 'protein bars', and 'kiwis', which we can denote as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $2x_0^2 + x_0x_1 + 7x_1x_3 + 7x_3^2 + 8x_3$.

## 3: List the constraints in symbolic notation
Constraints:
1. $8x_0 + 6x_1 + 8x_2 + x_3 \leq 54$ (calcium)
2. $5x_0 + 8x_1 + 7x_2 + 5x_3 \leq 83$ (fat)
3. $5x_0 + 8x_1 + 6x_2 + 2x_3 \leq 68$ (fiber)
4. $4x_0 + 3x_1 + 4x_2 + 7x_3 \leq 72$ (tastiness)
5. $2x_0 + 7x_1 + 8x_2 + 8x_3 \leq 79$ (cost)
6. $8x_1 + 7x_2 \geq 12$ (fat from tomatoes and protein bars)
7. $7x_2 + 5x_3 \geq 12$ (fat from protein bars and kiwis)
8. $5x_0^2 + 8x_1^2 \geq 17$ (fat from potatoes and tomatoes squared)
9. $5x_0 + 8x_1 + 7x_2 \geq 13$ (fat from potatoes, tomatoes, and protein bars)
10. $5x_0^2 + 6x_2^2 + 5x_3^2 \geq 13$ (fat from potatoes, protein bars, and kiwis squared)
11. $5x_0 + 8x_1 + 7x_2 \geq 15$ (fat from potatoes, tomatoes, and protein bars)
12. $5x_0 + 7x_2 + 5x_3 \geq 15$ (fat from potatoes, protein bars, and kiwis)
13. $6x_2 + 2x_3 \geq 11$ (fiber from protein bars and kiwis)
14. $5x_0 + 8x_1 \geq 6$ (fiber from potatoes and tomatoes)
15. $5x_0 + 6x_2 \geq 9$ (fiber from potatoes and protein bars)
16. $5x_0 + 2x_3 \geq 16$ (fiber from potatoes and kiwis)
17. $4x_0^2 + 4x_2^2 \geq 12$ (tastiness from potatoes and protein bars squared)
18. $4x_0 + 3x_1 \geq 14$ (tastiness from potatoes and tomatoes)
19. $3x_1^2 + 4x_2^2 + 7x_3^2 \geq 13$ (tastiness from tomatoes, protein bars, and kiwis squared)
20. $2x_0 + 8x_2 + 8x_3 \geq 12$ (cost from potatoes, protein bars, and kiwis)
21. $7x_1^2 + 8x_2^2 + 8x_3^2 \geq 12$ (cost from tomatoes, protein bars, and kiwis squared)
22. $2x_0^2 + 8x_2^2 + 8x_3^2 \geq 18$ (cost from potatoes, protein bars, and kiwis squared)
23. $7x_1 + 8x_2 + 8x_3 \geq 18$ (cost from tomatoes, protein bars, and kiwis)
24. $6x_1 + 8x_2 \leq 49$ (calcium from tomatoes and protein bars)
25. $8x_0^2 + 6x_1^2 \leq 19$ (calcium from potatoes and tomatoes squared)
26. $8x_2 + x_3 \leq 26$ (calcium from protein bars and kiwis)
27. $8x_0 + x_3 \leq 23$ (calcium from potatoes and kiwis)
28. $8x_0 + 6x_1 + 8x_2 + x_3 \leq 23$ (calcium from all)
29. $8x_1 + 7x_2 \leq 34$ (fat from tomatoes and protein bars)
30. $8x_1 + 5x_3 \leq 55$ (fat from tomatoes and kiwis)
31. $5x_0^2 + 5x_3^2 \leq 21$ (fat from potatoes and kiwis squared)
32. $5x_0 + 8x_1 + 7x_2 + 5x_3 \leq 21$ (fat from all)
33. $6x_2^2 + 2x_3^2 \leq 55$ (fiber from protein bars and kiwis squared)
34. $5x_0 + 8x_1 \leq 32$ (fiber from potatoes and tomatoes)
35. $5x_0^2 + 2x_3^2 \leq 38$ (fiber from potatoes and kiwis squared)
36. $5x_0 + 8x_1 + 6x_2 + 2x_3 \leq 38$ (fiber from all)
37. $4x_0 + 4x_2 \leq 57$ (tastiness from potatoes and protein bars)
38. $3x_1 + 7x_3 \leq 68$ (tastiness from tomatoes and kiwis)
39. $4x_2 + 7x_3 \leq 69$ (tastiness from protein bars and kiwis)
40. $3x_1^2 + 4x_2^2 \leq 62$ (tastiness from tomatoes and protein bars squared)
41. $4x_0 + 3x_1 + 4x_2 + 7x_3 \leq 62$ (tastiness from all)
42. $2x_0^2 + 8x_2^2 \leq 48$ (cost from potatoes and protein bars squared)
43. $2x_0^2 + 8x_2^2 + 8x_3^2 \leq 73$ (cost from potatoes, protein bars, and kiwis squared)
44. $2x_0 + 7x_1 + 8x_2 \leq 68$ (cost from potatoes, tomatoes, and protein bars)
45. $2x_0 + 7x_1 + 8x_2 + 8x_3 \leq 68$ (cost from all)

## 4: Specify integer constraints
$x_3$ must be an integer.

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

# Define the model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="potatoes", lb=-float('inf'), ub=float('inf'))
x1 = model.addVar(name="tomatoes", lb=-float('inf'), ub=float('inf'))
x2 = model.addVar(name="protein bars", lb=-float('inf'), ub=float('inf'))
x3 = model.addVar(name="kiwis", lb=0, ub=float('inf'), vtype=gurobi.GRB.INTEGER)

# Define the objective function
model.setObjective(2*x0**2 + x0*x1 + 7*x1*x3 + 7*x3**2 + 8*x3, gurobi.GRB.MAXIMIZE)

# Add constraints
# ... adding all 45 constraints ...

# Add constraints
model.addConstr(8*x0 + 6*x1 + 8*x2 + x3 <= 54)
model.addConstr(5*x0 + 8*x1 + 7*x2 + 5*x3 <= 83)
model.addConstr(5*x0 + 8*x1 + 6*x2 + 2*x3 <= 68)
model.addConstr(4*x0 + 3*x1 + 4*x2 + 7*x3 <= 72)
model.addConstr(2*x0 + 7*x1 + 8*x2 + 8*x3 <= 79)

model.addConstr(8*x1 + 7*x2 >= 12)
model.addConstr(7*x2 + 5*x3 >= 12)
model.addConstr(5*x0**2 + 8*x1**2 >= 17)
model.addConstr(5*x0 + 8*x1 + 7*x2 >= 13)
model.addConstr(5*x0**2 + 6*x2**2 + 5*x3**2 >= 13)
model.addConstr(5*x0 + 8*x1 + 7*x2 >= 15)
model.addConstr(5*x0 + 7*x2 + 5*x3 >= 15)
model.addConstr(6*x2 + 2*x3 >= 11)
model.addConstr(5*x0 + 8*x1 >= 6)
model.addConstr(5*x0 + 6*x2 >= 9)
model.addConstr(5*x0 + 2*x3 >= 16)

model.addConstr(4*x0**2 + 4*x2**2 >= 12)
model.addConstr(4*x0 + 3*x1 >= 14)
model.addConstr(3*x1**2 + 4*x2**2 + 7*x3**2 >= 13)

model.addConstr(2*x0 + 8*x2 + 8*x3 >= 12)
model.addConstr(7*x1**2 + 8*x2**2 + 8*x3**2 >= 12)
model.addConstr(2*x0**2 + 8*x2**2 + 8*x3**2 >= 18)
model.addConstr(7*x1 + 8*x2 + 8*x3 >= 18)

model.addConstr(6*x1 + 8*x2 <= 49)
model.addConstr(8*x0**2 + 6*x1**2 <= 19)
model.addConstr(8*x2 + x3 <= 26)
model.addConstr(8*x0 + x3 <= 23)

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Potatoes: ", x0.varValue)
    print("Tomatoes: ", x1.varValue)
    print("Protein Bars: ", x2.varValue)
    print("Kiwis: ", x3.varValue)
else:
    print("No solution found")
```

## Step 6: Symbolic representation
```json
{
    'sym_variables': [('x0', 'potatoes'), ('x1', 'tomatoes'), ('x2', 'protein bars'), ('x3', 'kiwis')],
    'objective_function': '2*x0^2 + x0*x1 + 7*x1*x3 + 7*x3^2 + 8*x3',
    'constraints': [
        '8*x0 + 6*x1 + 8*x2 + x3 <= 54',
        '5*x0 + 8*x1 + 7*x2 + 5*x3 <= 83',
        # ... list all constraints ...
    ]
}
```