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

**Decision Variables:**

* `x`: Number of beavers to make
* `y`: Number of bears to make

**Objective Function:**

Maximize profit: `5x + 7y`

**Constraints:**

* **Time Constraint:** `10x + 15y <= 2000` (Total production time cannot exceed 2000 minutes)
* **Beaver Demand Constraint:** `x >= 3y` (At least three times as many beavers as bears)
* **Non-negativity Constraints:** `x >= 0`, `y >= 0` (Cannot produce a negative number of toys)


```python
import gurobipy as gp

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

# Create variables
x = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="beavers") # Number of beavers, integer
y = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="bears")   # Number of bears, integer

# Set objective function
m.setObjective(5*x + 7*y, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(10*x + 15*y <= 2000, "time_constraint")
m.addConstr(x >= 3*y, "beaver_demand")

# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Number of Beavers (x): {x.x}")
    print(f"Number of Bears (y): {y.x}")
    print(f"Optimal Profit: {m.objVal}")
elif m.status == gp.GRB.INFEASIBLE:
    print("Model is infeasible.")
else:
    print(f"Optimization terminated with status {m.status}")

```
