To solve this optimization problem, we need to first translate the given natural language description into a symbolic representation. This involves identifying the variables, the objective function, and the constraints.

Given:
- Variables: `cornichons` and `peanutbutter sandwiches`
- Resources/Attributes:
  - `r0`: grams of fat with upper bound 103, where cornichons contribute 11 grams each and peanutbutter sandwiches contribute 10 grams each.
  - `r1`: dollar cost with upper bound 91, where cornichons cost $5 each and peanutbutter sandwiches cost $8 each.

Objective Function:
Maximize \(4x_0^2 + 6x_0x_1 + 3x_1^2 + 4x_0 + 2x_1\), where \(x_0\) represents the number of cornichons and \(x_1\) represents the number of peanutbutter sandwiches.

Constraints:
1. Total fat from cornichons and peanutbutter sandwiches must be at least 22 grams: \(11x_0 + 10x_1 \geq 22\)
2. Minimum cost of $21: \(5x_0 + 8x_1 \geq 21\)
3. \(6x_0^2 - 3x_1^2 \geq 0\)
4. Total fat from cornichons and peanutbutter sandwiches must not exceed 62 grams: \(11x_0 + 10x_1 \leq 62\)
5. Maximum cost of $59: \(5x_0 + 8x_1 \leq 59\)
6. Whole number of cornichons: \(x_0 \in \mathbb{Z}\)
7. Non-fractional number of peanutbutter sandwiches: \(x_1 \in \mathbb{Z}\)

Symbolic Representation:
```json
{
  'sym_variables': [('x0', 'cornichons'), ('x1', 'peanutbutter sandwiches')],
  'objective_function': '4*x0**2 + 6*x0*x1 + 3*x1**2 + 4*x0 + 2*x1',
  'constraints': [
    '11*x0 + 10*x1 >= 22',
    '5*x0 + 8*x1 >= 21',
    '6*x0**2 - 3*x1**2 >= 0',
    '11*x0 + 10*x1 <= 62',
    '5*x0 + 8*x1 <= 59'
  ]
}
```

To implement this in Gurobi, we will use the Python interface. Here is how you can do it:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Add variables
x0 = m.addVar(vtype=GRB.INTEGER, name="cornichons")
x1 = m.addVar(vtype=GRB.INTEGER, name="peanutbutter_sandwiches")

# Set the objective function
m.setObjective(4*x0**2 + 6*x0*x1 + 3*x1**2 + 4*x0 + 2*x1, GRB.MAXIMIZE)

# Add constraints
m.addConstr(11*x0 + 10*x1 >= 22, name="min_fat")
m.addConstr(5*x0 + 8*x1 >= 21, name="min_cost")
m.addConstr(6*x0**2 - 3*x1**2 >= 0, name="fat_constraint")
m.addConstr(11*x0 + 10*x1 <= 62, name="max_fat")
m.addConstr(5*x0 + 8*x1 <= 59, name="max_cost")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"cornichons: {x0.x}")
    print(f"peanutbutter sandwiches: {x1.x}")
    print(f"Objective value: {m.objVal}")
else:
    print("No optimal solution found")
```