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 washing machines to be installed as \(x_1\) and the number of dryers to be installed as \(x_2\).

The symbolic representation of the variables is:
- \(x_1\): Number of washing machines
- \(x_2\): Number of dryers

The objective function, which represents the total profit, can be written as:
\[200x_1 + 150x_2\]

This is because each washing machine installation yields a profit of $200 and each dryer installation yields a profit of $150.

The constraints are based on the available time for plumbers and electricians. Each washing machine requires 20 minutes of plumber time and 15 minutes of electrician time, while each dryer requires 10 minutes of plumber time and 25 minutes of electrician time. The total available time is 2000 minutes for plumbers and 3000 minutes for electricians. Thus, the constraints can be written as:
1. \(20x_1 + 10x_2 \leq 2000\) (Plumber time constraint)
2. \(15x_1 + 25x_2 \leq 3000\) (Electrician time constraint)
3. \(x_1, x_2 \geq 0\) (Non-negativity constraints, as the number of installations cannot be negative)

In symbolic notation with natural language objects, we have:
```json
{
  'sym_variables': [('x1', 'Number of washing machines'), ('x2', 'Number of dryers')],
  'objective_function': '200*x1 + 150*x2',
  'constraints': ['20*x1 + 10*x2 <= 2000', '15*x1 + 25*x2 <= 3000', 'x1 >= 0', 'x2 >= 0']
}
```

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

```python
from gurobipy import *

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

# Create variables
x1 = m.addVar(name="washing_machines", vtype=GRB.INTEGER, lb=0)
x2 = m.addVar(name="dryers", vtype=GRB.INTEGER, lb=0)

# Set the objective function
m.setObjective(200*x1 + 150*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(20*x1 + 10*x2 <= 2000, name="plumber_time")
m.addConstr(15*x1 + 25*x2 <= 3000, name="electrician_time")

# Optimize the model
m.optimize()

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