Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

* `x`: Number of plush toys produced.
* `y`: Number of action figures produced.

**Objective Function:**

Maximize profit:  `4x + 4.5y`

**Constraints:**

* Assembly time: `20x + 15y <= 1200`
* Packaging time: `4x + 5y <= 900`
* Non-negativity: `x >= 0`, `y >= 0`


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

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

# Create decision variables
x = model.addVar(vtype=GRB.CONTINUOUS, name="plush_toys")  # Plush toys
y = model.addVar(vtype=GRB.CONTINUOUS, name="action_figures") # Action figures

# Set objective function
model.setObjective(4*x + 4.5*y, GRB.MAXIMIZE)

# Add constraints
model.addConstr(20*x + 15*y <= 1200, "assembly_time")
model.addConstr(4*x + 5*y <= 900, "packaging_time")
model.addConstr(x >= 0, "plush_non_neg")
model.addConstr(y >= 0, "action_non_neg")

# Optimize model
model.optimize()

# Print results
if model.status == GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"  Plush Toys: {x.x}")
    print(f"  Action Figures: {y.x}")
    print(f"  Maximum Profit: ${model.objVal}")
elif model.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status {model.status}")

```
