Here's how we can formulate this problem and translate it into Gurobi code:

**Decision Variables:**

* `x`: Number of bottles of Eucalyptus lotion stocked.
* `y`: Number of bottles of Citrus lotion stocked.

**Objective Function:**

Maximize profit: `1x + 4y`

**Constraints:**

* **Budget Constraint:** `6x + 8y <= 10000` (The total cost of inventory should not exceed $10,000)
* **Demand Constraint:** `x + y <= 1500` (The total number of bottles stocked should not exceed 1500)
* **Non-negativity Constraints:** `x >= 0`, `y >= 0` (The number of bottles stocked cannot be negative)


```python
import gurobipy as gp
from gurobipy import GRB

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

# Create decision variables
x = m.addVar(vtype=GRB.INTEGER, name="Eucalyptus")
y = m.addVar(vtype=GRB.INTEGER, name="Citrus")

# Set objective function
m.setObjective(1*x + 4*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(6*x + 8*y <= 10000, "Budget")
m.addConstr(x + y <= 1500, "Demand")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Number of Eucalyptus bottles: {x.x}")
    print(f"Number of Citrus bottles: {y.x}")
    print(f"Maximum Profit: ${m.objVal}")
elif m.status == GRB.INFEASIBLE:
    print("Model is infeasible. No solution found.")
else:
    print(f"Optimization terminated with status {m.status}")

```
