## Problem Description and Formulation

The problem involves allocating resources at two plants, Gamma and Delta, to produce two products: asphalt and bricks. The goal is to minimize the cost of meeting the daily demands of at least 90 units of asphalt and 85 units of bricks.

### Decision Variables

Let \(x_\gamma\) be the number of hours plant Gamma operates and \(x_\delta\) be the number of hours plant Delta operates.

### Objective Function

The objective is to minimize the total cost. The cost of running plant Gamma is $35 per hour, and the cost of running plant Delta is $95 per hour. Therefore, the objective function can be written as:

\[ \text{Minimize:} \quad 35x_\gamma + 95x_\delta \]

### Constraints

1. **Asphalt Demand:** Plant Gamma yields 4 units of asphalt per hour, and plant Delta yields 6 units of asphalt per hour. The demand is for at least 90 units of asphalt daily.

\[ 4x_\gamma + 6x_\delta \geq 90 \]

2. **Bricks Demand:** Plant Gamma yields 3 units of bricks per hour, and plant Delta yields 5 units of bricks per hour. The demand is for at least 85 units of bricks daily.

\[ 3x_\gamma + 5x_\delta \geq 85 \]

3. **Non-Negativity:** The number of hours the plants operate cannot be negative.

\[ x_\gamma \geq 0, \quad x_\delta \geq 0 \]

## Gurobi Code

```python
import gurobi

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

    # Decision variables
    x_gamma = model.addVar(name="Gamma_hours", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x_delta = model.addVar(name="Delta_hours", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: Minimize cost
    model.setObjective(35 * x_gamma + 95 * x_delta, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(4 * x_gamma + 6 * x_delta >= 90, name="Asphalt_demand")
    model.addConstr(3 * x_gamma + 5 * x_delta >= 85, name="Bricks_demand")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Gamma hours: {x_gamma.varValue}")
        print(f"Delta hours: {x_delta.varValue}")
        print(f"Total Cost: {model.objVal}")
    else:
        print("The model is infeasible")

solve_production_planning()
```