To solve this problem, we first need to define the decision variables and the objective function. Let's denote the number of toques as \(T\) and the number of scarves as \(S\). The objective is to maximize profit, which can be calculated as \(5T + 7S\), given that each toque brings in $5 and each scarf brings in $7.

The constraints are based on the availability of yarn and time. For yarn, since a toque requires 3 units and a scarf requires 5 units, and there are 200 units available, we have \(3T + 5S \leq 200\). For time, with each toque requiring 30 minutes and each scarf requiring 40 minutes, and 1800 minutes available, we get \(30T + 40S \leq 1800\).

Additionally, \(T\) and \(S\) must be non-negative since the man cannot knit a negative number of items.

Now, let's translate this into Gurobi code in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Knitting_Optimization")

# Define variables
T = m.addVar(name="Toques", vtype=GRB.INTEGER, lb=0)
S = m.addVar(name="Scarves", vtype=GRB.INTEGER, lb=0)

# Set the objective function: Maximize profit
m.setObjective(5*T + 7*S, GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*T + 5*S <= 200, name="Yarn_Constraint")
m.addConstr(30*T + 40*S <= 1800, name="Time_Constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: {T.varName} = {T.x}, {S.varName} = {S.x}")
    print(f"Maximum profit: ${5*T.x + 7*S.x}")
else:
    print("No optimal solution found")
```