## Problem Description and Formulation

The problem is a linear programming optimization problem. The goal is to maximize the profit of a furniture company that produces regular refrigerators and energy-efficient refrigerators. The company faces the following constraints:

- Demand constraints: at least 25 regular refrigerators and 40 energy-efficient refrigerators must be produced each day.
- Production capacity constraints: at most 100 regular refrigerators and 70 energy-efficient refrigerators can be produced per day.
- Total production constraint: a minimum of 90 refrigerators must be produced each day.

The profit per regular refrigerator is $50, and the profit per energy-efficient refrigerator is $80.

## Decision Variables

Let \(R\) be the number of regular refrigerators produced and \(E\) be the number of energy-efficient refrigerators produced.

## Objective Function

The objective is to maximize the total profit \(P = 50R + 80E\).

## Constraints

1. \(R \geq 25\) (demand for regular refrigerators)
2. \(E \geq 40\) (demand for energy-efficient refrigerators)
3. \(R \leq 100\) (production capacity for regular refrigerators)
4. \(E \leq 70\) (production capacity for energy-efficient refrigerators)
5. \(R + E \geq 90\) (total production requirement)

## Gurobi Code

```python
import gurobi

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

    # Define decision variables
    R = model.addVar(lb=25, ub=100, name="Regular_Refrigerators")
    E = model.addVar(lb=40, ub=70, name="Energy_Efficient_Refrigerators")

    # Objective function: maximize profit
    model.setObjective(50*R + 80*E, gurobi.GRB.MAXIMIZE)

    # Additional constraint: total production
    model.addConstraint(R + E >= 90)

    # Solve the model
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal production: Regular={R.varValue}, Energy Efficient={E.varValue}")
        print(f"Max Profit: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_refrigerator_problem()
```