## Step 1: Define the symbolic representation of the variables
The variables are ['potatoes', 'hamburgers', 'peanutbutter sandwiches', 'strawberries']. Let's denote them as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is: $1 \cdot x_1^2 + 7 \cdot x_1 \cdot x_4 + 1 \cdot x_2 \cdot x_4 + 4 \cdot x_3^2 + 5 \cdot x_1 + 7 \cdot x_3$.

## Step 3: List the constraints in symbolic notation
Constraints:
1. $0.65x_1 \leq 121$
2. $0.59x_1 \leq 137$
3. $0.23x_1 \leq 125$
4. $0.89x_2 \leq 121$
5. $0.85x_2 \leq 137$
6. $0.64x_2 \leq 125$
7. $0.32x_3 \leq 121$
8. $0.39x_3 \leq 137$
9. $0.89x_3 \leq 125$
10. $0.62x_4 \leq 121$
11. $0.0x_4 \leq 137$
12. $0.18x_4 \leq 125$
13. $0.89x_2^2 + 0.62x_4^2 \geq 13$
14. $0.65x_1 + 0.32x_3 + 0.62x_4 \geq 19$
15. $0.64x_2 + 0.89x_3 \geq 13$
16. $8x_1 - 8x_2 - 8x_3 \geq 0$
17. $0.65x_1 + 0.32x_3 \leq 76$
18. $0.89x_2^2 + 0.62x_4^2 \leq 95$
19. $0.32x_3^2 + 0.62x_4^2 \leq 35$
20. $0.65x_1 + 0.89x_2 + 0.32x_3 + 0.62x_4 \leq 35$
21. $0.39x_3 + 0.0x_4 \leq 86$
22. $0.59x_1 + 0.0x_4 \leq 103$
23. $0.59x_1 + 0.39x_3 + 0.0x_4 \leq 78$
24. $0.59x_1 + 0.85x_2 + 0.39x_3 \leq 128$
25. $0.85x_2 + 0.39x_3 + 0.0x_4 \leq 131$
26. $0.59x_1 + 0.85x_2 + 0.39x_3 + 0.0x_4 \leq 131$
27. $0.64x_2 + 0.89x_3 \leq 73$
28. $0.23x_1 + 0.18x_4 \leq 38$
29. $0.23x_1 + 0.89x_3 \leq 82$
30. $0.89x_3 + 0.18x_4 \leq 44$
31. $0.23x_1 + 0.89x_3 + 0.18x_4 \leq 89$
32. $0.23x_1 + 0.64x_2 + 0.18x_4 \leq 70$
33. $0.23x_1 + 0.64x_2 + 0.89x_3 + 0.18x_4 \leq 70$

## Step 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'potatoes'), 
        ('x2', 'hamburgers'), 
        ('x3', 'peanutbutter sandwiches'), 
        ('x4', 'strawberries')
    ], 
    'objective_function': '1*x1^2 + 7*x1*x4 + 1*x2*x4 + 4*x3^2 + 5*x1 + 7*x3', 
    'constraints': [
        '0.65*x1 <= 121',
        '0.59*x1 <= 137',
        '0.23*x1 <= 125',
        '0.89*x2 <= 121',
        '0.85*x2 <= 137',
        '0.64*x2 <= 125',
        '0.32*x3 <= 121',
        '0.39*x3 <= 137',
        '0.89*x3 <= 125',
        '0.62*x4 <= 121',
        '0.0*x4 <= 137',
        '0.18*x4 <= 125',
        '0.89*x2^2 + 0.62*x4^2 >= 13',
        '0.65*x1 + 0.32*x3 + 0.62*x4 >= 19',
        '0.64*x2 + 0.89*x3 >= 13',
        '8*x1 - 8*x2 - 8*x3 >= 0',
        '0.65*x1 + 0.32*x3 <= 76',
        '0.89*x2^2 + 0.62*x4^2 <= 95',
        '0.32*x3^2 + 0.62*x4^2 <= 35',
        '0.65*x1 + 0.89*x2 + 0.32*x3 + 0.62*x4 <= 35',
        '0.39*x3 + 0.0*x4 <= 86',
        '0.59*x1 + 0.0*x4 <= 103',
        '0.59*x1 + 0.39*x3 + 0.0*x4 <= 78',
        '0.59*x1 + 0.85*x2 + 0.39*x3 <= 128',
        '0.85*x2 + 0.39*x3 + 0.0*x4 <= 131',
        '0.59*x1 + 0.85*x2 + 0.39*x3 + 0.0*x4 <= 131',
        '0.64*x2 + 0.89*x3 <= 73',
        '0.23*x1 + 0.18*x4 <= 38',
        '0.23*x1 + 0.89*x3 <= 82',
        '0.89*x3 + 0.18*x4 <= 44',
        '0.23*x1 + 0.89*x3 + 0.18*x4 <= 89',
        '0.23*x1 + 0.64*x2 + 0.18*x4 <= 70',
        '0.23*x1 + 0.64*x2 + 0.89*x3 + 0.18*x4 <= 70'
    ]
}
```

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

# Define the model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name='potatoes', vtype=gurobi.GRB.INTEGER, lb=0)
x2 = m.addVar(name='hamburgers', vtype=gurobi.GRB.CONTINUOUS, lb=0)
x3 = m.addVar(name='peanutbutter sandwiches', vtype=gurobi.GRB.INTEGER, lb=0)
x4 = m.addVar(name='strawberries', vtype=gurobi.GRB.CONTINUOUS, lb=0)

# Objective function
m.setObjective(1 * x1**2 + 7 * x1 * x4 + 1 * x2 * x4 + 4 * x3**2 + 5 * x1 + 7 * x3, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(0.65 * x1 <= 121)
m.addConstr(0.59 * x1 <= 137)
m.addConstr(0.23 * x1 <= 125)
m.addConstr(0.89 * x2 <= 121)
m.addConstr(0.85 * x2 <= 137)
m.addConstr(0.64 * x2 <= 125)
m.addConstr(0.32 * x3 <= 121)
m.addConstr(0.39 * x3 <= 137)
m.addConstr(0.89 * x3 <= 125)
m.addConstr(0.62 * x4 <= 121)
m.addConstr(0.0 * x4 <= 137)
m.addConstr(0.18 * x4 <= 125)
m.addConstr(0.89 * x2**2 + 0.62 * x4**2 >= 13)
m.addConstr(0.65 * x1 + 0.32 * x3 + 0.62 * x4 >= 19)
m.addConstr(0.64 * x2 + 0.89 * x3 >= 13)
m.addConstr(8 * x1 - 8 * x2 - 8 * x3 >= 0)
m.addConstr(0.65 * x1 + 0.32 * x3 <= 76)
m.addConstr(0.89 * x2**2 + 0.62 * x4**2 <= 95)
m.addConstr(0.32 * x3**2 + 0.62 * x4**2 <= 35)
m.addConstr(0.65 * x1 + 0.89 * x2 + 0.32 * x3 + 0.62 * x4 <= 35)
m.addConstr(0.39 * x3 + 0.0 * x4 <= 86)
m.addConstr(0.59 * x1 + 0.0 * x4 <= 103)
m.addConstr(0.59 * x1 + 0.39 * x3 + 0.0 * x4 <= 78)
m.addConstr(0.59 * x1 + 0.85 * x2 + 0.39 * x3 <= 128)
m.addConstr(0.85 * x2 + 0.39 * x3 + 0.0 * x4 <= 131)
m.addConstr(0.59 * x1 + 0.85 * x2 + 0.39 * x3 + 0.0 * x4 <= 131)
m.addConstr(0.64 * x2 + 0.89 * x3 <= 73)
m.addConstr(0.23 * x1 + 0.18 * x4 <= 38)
m.addConstr(0.23 * x1 + 0.89 * x3 <= 82)
m.addConstr(0.89 * x3 + 0.18 * x4 <= 44)
m.addConstr(0.23 * x1 + 0.89 * x3 + 0.18 * x4 <= 89)
m.addConstr(0.23 * x1 + 0.64 * x2 + 0.18 * x4 <= 70)
m.addConstr(0.23 * x1 + 0.64 * x2 + 0.89 * x3 + 0.18 * x4 <= 70)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('Potatoes: ', x1.varValue)
    print('Hamburgers: ', x2.varValue)
    print('Peanutbutter sandwiches: ', x3.varValue)
    print('Strawberries: ', x4.varValue)
else:
    print('No optimal solution found')
```