## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The repairman needs to decide how many fridges and ovens to fix in order to maximize his earnings, given the limited time available for inspection and fixing.

Let's define the decision variables:

* `x`: number of fridges to fix
* `y`: number of ovens to fix

The objective function is to maximize the total earnings:

* `100x + 125y`: total earnings

The constraints are:

* Inspection time: `20x + 30y <= 1000` (1000 minutes available for inspection)
* Fixing time: `30x + 15y <= 800` (800 minutes available for fixing)
* Non-negativity: `x >= 0`, `y >= 0` (number of fridges and ovens cannot be negative)

## Gurobi Code

```python
import gurobi

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

    # Define the decision variables
    x = model.addVar(name="fridges", lb=0, ub=None, obj=100)
    y = model.addVar(name="ovens", lb=0, ub=None, obj=125)

    # Add inspection time constraint
    model.addConstr(20*x + 30*y <= 1000, name="inspection_time")

    # Add fixing time constraint
    model.addConstr(30*x + 15*y <= 800, name="fixing_time")

    # Set the objective function
    model.setObjective(x.obj * x + y.obj * y, gurobi.GRB.MAXIMIZE)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of fridges to fix: {x.x}")
        print(f"Number of ovens to fix: {y.x}")
        print(f"Total earnings: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_repairman_problem()
```

However, note that in the code above, I used the `obj` attribute of the variables when setting up the objective function which is incorrect as it doesn't account for multiplying by the variable itself. The right way is to use `model.setObjective` with a linear expression.

Here's the corrected code:

```python
import gurobi

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

    # Define the decision variables
    x = model.addVar(name="fridges", lb=0, ub=None)
    y = model.addVar(name="ovens", lb=0, ub=None)

    # Add inspection time constraint
    model.addConstr(20*x + 30*y <= 1000, name="inspection_time")

    # Add fixing time constraint
    model.addConstr(30*x + 15*y <= 800, name="fixing_time")

    # Set the objective function
    model.setObjective(100*x + 125*y, gurobi.GRB.MAXIMIZE)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of fridges to fix: {x.x}")
        print(f"Number of ovens to fix: {y.x}")
        print(f"Total earnings: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_repairman_problem()
```