## Problem Description and Formulation

The problem described is a classic example of a linear programming problem. The woodshop aims to maximize profit by determining the optimal number of dining tables and desks to produce, given the constraints on available resources (woodworking hours, boxes of nails, and units of varnish).

Let's define the decision variables:
- \(x\): the number of dining tables to be made
- \(y\): the number of desks to be made

The objective function to maximize profit (\(P\)) is:
\[ P = 350x + 400y \]

The constraints based on the available resources are:
1. Woodworking: \(2x + 3y \leq 100\)
2. Nails: \(3x + 4y \leq 75\)
3. Varnish: \(x + 2y \leq 80\)
4. Non-negativity: \(x \geq 0, y \geq 0\)

## Gurobi Code

To solve this problem using Gurobi in Python, we will use the Gurobi Python API. First, ensure you have Gurobi installed in your Python environment. You can install it via pip:
```bash
pip install gurobi
```

Here's the Gurobi code to solve the problem:

```python
import gurobi as gp

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

# Define the decision variables
x = model.addVar(name="dining_tables", lb=0, vtype=gp.GRB.CONTINUOUS)
y = model.addVar(name="desks", lb=0, vtype=gp.GRB.CONTINUOUS)

# Define the objective function
model.setObjective(350 * x + 400 * y, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(2 * x + 3 * y <= 100, name="woodworking_constraint")
model.addConstr(3 * x + 4 * y <= 75, name="nails_constraint")
model.addConstr(x + 2 * y <= 80, name="varnish_constraint")

# Optimize the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution found. Profit: ${model.objVal:.2f}")
    print(f"Dining tables to make: {x.varValue:.2f}")
    print(f"Desks to make: {y.varValue:.2f}")
else:
    print("No optimal solution found.")
```

This code sets up the optimization problem as described, solves it using Gurobi, and then prints out the optimal solution if one is found, including the number of dining tables and desks to make and the maximum achievable profit.