To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. Let's denote the number of acres for mangoes as $x_1$ and the number of acres for pineapples as $x_2$. The objective is to maximize profit.

Given:
- Each acre of mangoes costs $80 for nutrients.
- Each acre of pineapples costs $100 for nutrients.
- The farmer has $18,000 available for nutrients.
- Each acre of mangoes takes 2 hours for picking.
- Each acre of pineapples takes 1.5 hours for picking.
- The farmer has 350 hours available for picking.
- Profit per acre of mangoes is $400.
- Profit per acre of pineapples is $450.

Symbolic Representation:
```json
{
    'sym_variables': [('x1', 'acres of mangoes'), ('x2', 'acres of pineapples')],
    'objective_function': '400*x1 + 450*x2',
    'constraints': [
        '80*x1 + 100*x2 <= 18000',  # Nutrient cost constraint
        '2*x1 + 1.5*x2 <= 350',     # Picking time constraint
        'x1 + x2 <= 200',           # Total land constraint
        'x1 >= 0',                  # Non-negativity constraint for mangoes
        'x2 >= 0'                   # Non-negativity constraint for pineapples
    ]
}
```

Now, let's implement this optimization problem using Gurobi in Python:

```python
from gurobipy import *

# Create a model
m = Model("Tropical_Farmer")

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="acres_of_mangoes")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="acres_of_pineapples")

# Set the objective function
m.setObjective(400*x1 + 450*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(80*x1 + 100*x2 <= 18000, "nutrient_cost")
m.addConstr(2*x1 + 1.5*x2 <= 350, "picking_time")
m.addConstr(x1 + x2 <= 200, "total_land")
m.addConstr(x1 >= 0, "non_neg_mangoes")
m.addConstr(x2 >= 0, "non_neg_pineapples")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Maximum Profit: {m.objVal}")
else:
    print("No optimal solution found")
```