## Problem Description and Formulation

The problem is a linear programming optimization problem. The goal is to maximize the total revenue of a keyboard company that produces two types of analog synthesizer keyboards: one with 61 keys and another with 81 keys. The selling prices of these keyboards are $1500 and $2500, respectively.

### Decision Variables

Let \(x_1\) be the number of 61-key keyboards produced and \(x_2\) be the number of 81-key keyboards produced.

### Objective Function

The objective is to maximize the total revenue. The revenue from selling \(x_1\) units of the 61-key keyboard is \(1500x_1\) and from selling \(x_2\) units of the 81-key keyboard is \(2500x_2\). Therefore, the total revenue \(R\) is given by:
\[ R = 1500x_1 + 2500x_2 \]

### Constraints

1. **Oscillator Chip Constraint**: There are 3000 oscillator chips available daily. The 61-key keyboard requires 8 chips, and the 81-key keyboard requires 16 chips. Therefore:
\[ 8x_1 + 16x_2 \leq 3000 \]

2. **Production Time Constraint**: There are 8 working hours a day, and each keyboard requires 1.5 hours of production time. Therefore:
\[ 1.5x_1 + 1.5x_2 \leq 8 \times 60 \]

   However, to maintain consistency with common units (typically hours for such problems), let's adjust this constraint for clarity and accuracy in representation:
\[ 1.5x_1 + 1.5x_2 \leq 480 \]

3. **Non-Negativity Constraint**: The production quantities cannot be negative:
\[ x_1 \geq 0, x_2 \geq 0 \]

## Gurobi Code

```python
import gurobi

def solve_keyboard_production():
    # Create a new model
    model = gurobi.Model()

    # Decision variables
    x1 = model.addVar(lb=0, name="61_key_keyboard")
    x2 = model.addVar(lb=0, name="81_key_keyboard")

    # Objective function: Maximize total revenue
    model.setObjective(1500*x1 + 2500*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(8*x1 + 16*x2 <= 3000, name="oscillator_chips")
    model.addConstr(1.5*x1 + 1.5*x2 <= 480, name="production_time")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal production quantities:")
        print(f"61-key keyboards: {x1.varValue}")
        print(f"81-key keyboards: {x2.varValue}")
        print(f"Max Revenue: {model.objVal}")
    else:
        print("The problem is infeasible")

solve_keyboard_production()
```