To solve the given optimization problem using Gurobi, we first need to translate the natural language description into a mathematical formulation. The objective is to maximize the function:

7.59 * (peanutbutter sandwiches)^2 + 1.23 * (cheeseburgers)^2 + 3.08 * (bagged salads)^2

Subject to several constraints related to carbohydrate intake from each food item, both individually and in combination.

Let's denote:
- x0 as the number of peanutbutter sandwiches,
- x1 as the number of cheeseburgers,
- x2 as the number of bagged salads.

Given data:
- Each peanutbutter sandwich contains 21 grams of carbohydrates.
- Each cheeseburger contains 22 grams of carbohydrates.
- Each bagged salad contains 11 grams of carbohydrates.

Constraints:
1. Carbohydrates from peanutbutter sandwiches squared and cheeseburgers squared: 21*x0^2 + 22*x1^2 <= 204
2. Carbohydrates from peanutbutter sandwiches squared and bagged salads squared: 21*x0^2 + 11*x2^2 <= 312
3. Carbohydrates from cheeseburgers squared and bagged salads squared: 22*x1^2 + 11*x2^2 <= 298
4. Total carbohydrates from all sources: 21*x0 + 22*x1 + 11*x2 <= 298

Variable restrictions:
- x0 (peanutbutter sandwiches) can be a non-whole number.
- x1 (cheeseburgers) must be a whole number.
- x2 (bagged salads) can be a decimal.

Here is the Gurobi code to solve this problem:

```python
from gurobipy import *

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

# Define variables, considering the restrictions
x0 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="peanutbutter_sandwiches")
x1 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.INTEGER, name="cheeseburgers")
x2 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="bagged_salads")

# Define the objective function
m.setObjective(7.59 * x0**2 + 1.23 * x1**2 + 3.08 * x2**2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(21*x0**2 + 22*x1**2 <= 204, name="carb_pbs_cb")
m.addConstr(21*x0**2 + 11*x2**2 <= 312, name="carb_pbs_bs")
m.addConstr(22*x1**2 + 11*x2**2 <= 298, name="carb_cb_bs")
m.addConstr(21*x0 + 22*x1 + 11*x2 <= 298, name="total_carb")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"peanutbutter_sandwiches: {x0.x}")
    print(f"cheeseburgers: {x1.x}")
    print(f"bagged_salads: {x2.x}")
else:
    print("No optimal solution found")
```