## Problem Description and Formulation

The problem requires minimizing an objective function subject to several constraints. The objective function to be minimized is:

\[ 1 \times \text{kiwis}^2 + 3 \times \text{kiwis} \times \text{strawberries} + 7 \times \text{strawberries}^2 + 9 \times \text{kiwis} + 3 \times \text{strawberries} \]

The constraints are:

1. **Tastiness Ratings**:
   - Kiwi tastiness rating: 1.97
   - Strawberry tastiness rating: 4.63

2. **Minimum Combined Tastiness Rating**:
   - The total combined tastiness rating from kiwis and strawberries must be at least 71.

3. **Maximum Combined Tastiness Rating**:
   - The total combined tastiness rating from kiwis and strawberries must be no more than 138.

4. **Quadratic Constraint**:
   - \(8 \times \text{kiwis}^2 - 8 \times \text{strawberries}^2 \geq 0\)

5. **Variable Constraints**:
   - Kiwi quantity can be a non-whole number.
   - Strawberry quantity must be a whole number.

## Gurobi Code Formulation

```python
import gurobipy as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define variables
kiwis = m.addVar(lb=-gp.GRB.INFINITY, name="kiwis")  # No lower bound specified, assuming can be negative
strawberries = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="strawberries")  # Must be a whole number

# Objective function
m.setObjective(kiwis**2 + 3*kiwis*strawberries + 7*strawberries**2 + 9*kiwis + 3*strawberries, gp.GRB.MINIMIZE)

# Constraints
tastiness_kiwi = 1.97
tastiness_strawberry = 4.63

m.addConstr(tastiness_kiwi * kiwis + tastiness_strawberry * strawberries >= 71, name="min_tastiness")
m.addConstr(tastiness_kiwi * kiwis + tastiness_strawberry * strawberries <= 138, name="max_tastiness")
m.addConstr(8 * kiwis**2 - 8 * strawberries**2 >= 0, name="quadratic_constraint")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Kiwis: {kiwis.varValue}")
    print(f"Strawberries: {strawberries.varValue}")
    print(f"Objective: {m.objVal}")
else:
    print("No optimal solution found.")
```

This code captures the problem description and provides a solution using Gurobi. If the problem is infeasible, it will indicate so. Note that the variable `kiwis` has no specified lower bound, assuming it can be negative. If there's a specific lower bound, you should adjust the `lb` parameter when adding the variable.