## Symbolic Representation

To solve the given problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, as well as the constraints.

- Let \(x_1\) be the number of washing machines installed.
- Let \(x_2\) be the number of dryers installed.

The objective is to maximize profit. Given that the profit per washing machine installation is $200 and per dryer installation is $150, the objective function can be written as:

\[ \text{Maximize:} \quad 200x_1 + 150x_2 \]

The constraints are based on the available time for plumbers and electricians:

- Each washing machine takes 20 minutes of plumber time, and each dryer takes 10 minutes. The total available plumber time is 2000 minutes. So, the plumber time constraint is:
\[ 20x_1 + 10x_2 \leq 2000 \]

- Each washing machine takes 15 minutes of electrician time, and each dryer takes 25 minutes. The total available electrician time is 3000 minutes. So, the electrician time constraint is:
\[ 15x_1 + 25x_2 \leq 3000 \]

Also, \(x_1 \geq 0\) and \(x_2 \geq 0\) because the number of installations cannot be negative.

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'washing machines'), ('x2', 'dryers')],
    'objective_function': '200*x1 + 150*x2',
    'constraints': [
        '20*x1 + 10*x2 <= 2000',
        '15*x1 + 25*x2 <= 3000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="washing_machines", lb=0, vtype=gp.GRB.INTEGER)
x2 = model.addVar(name="dryers", lb=0, vtype=gp.GRB.INTEGER)

# Objective function: maximize profit
model.setObjective(200*x1 + 150*x2, gp.GRB.MAXIMIZE)

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

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal number of washing machines: {x1.varValue}")
    print(f"Optimal number of dryers: {x2.varValue}")
    print(f"Maximum profit: ${model.objVal:.2f}")
else:
    print("The model is infeasible.")
```