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

**Decision Variables:**

* `x`: Number of glass jars packaged.
* `y`: Number of plates packaged.

**Objective Function:**

Maximize profit:  `2x + 2.5y`

**Constraints:**

* Worker time: `15x + 12y <= 620`
* Cardboard: `3x + 4y <= 120`
* Non-negativity: `x >= 0`, `y >= 0`


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

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

# Create variables
x = m.addVar(vtype=GRB.CONTINUOUS, name="jars")  # jars
y = m.addVar(vtype=GRB.CONTINUOUS, name="plates") # plates

# Set objective
m.setObjective(2*x + 2.5*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(15*x + 12*y <= 620, "worker_time")
m.addConstr(3*x + 4*y <= 120, "cardboard")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal profit: ${m.objVal:.2f}")
    print(f"Number of jars to package: {x.x:.2f}")
    print(f"Number of plates to package: {y.x:.2f}")
elif m.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization ended with status {m.status}")

```
