Here's the Gurobi code to solve the optimization problem.  We've translated the objective and constraints into the appropriate Gurobi syntax. Note that the objective function is nonlinear (quadratic). We've also incorporated the variable types (continuous for fruit salads, integer for potatoes).

```python
from gurobipy import Model, GRB

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

# Create variables
fruit_salads = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="fruit_salads")
potatoes = m.addVar(lb=0, vtype=GRB.INTEGER, name="potatoes")

# Set objective function
m.setObjective(8.83 * fruit_salads**2 + 6.48 * fruit_salads * potatoes + 3.67 * fruit_salads + 6.4 * potatoes, GRB.MAXIMIZE)

# Add constraints
m.addConstr(12 * fruit_salads + 8 * potatoes >= 25, "fat_min")
m.addConstr(8 * fruit_salads**2 + 15 * potatoes**2 >= 52, "iron_min_squared")
m.addConstr(fruit_salads**2 - 10 * potatoes**2 >= 0, "fruit_potatoes_relation")
m.addConstr(12 * fruit_salads**2 + 8 * potatoes**2 <= 63, "fat_max_squared")
m.addConstr(12 * fruit_salads + 8 * potatoes <= 63, "fat_max")
m.addConstr(8 * fruit_salads + 15 * potatoes <= 141, "iron_max")


# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    print('fruit_salads:', fruit_salads.x)
    print('potatoes:', potatoes.x)
elif m.status == GRB.INFEASIBLE:
    print('Optimization problem is infeasible.')
else:
    print('Optimization ended with status %d' % m.status)

```
