To solve this optimization problem, we first need to define our decision variables and constraints. Let's denote:

- \(x\) as the number of cutting boards made.
- \(y\) as the number of chairs made.

Our objective is to maximize profit. Given that each cutting board gives a profit of $14 and each chair gives a profit of $25, our objective function can be written as:

\[ \text{Maximize:} \quad 14x + 25y \]

Now, let's define the constraints based on the given information:

1. **Time Constraint**: Each cutting board takes 30 minutes to make, and each chair takes 70 minutes to make. The total available time is 1500 minutes.

\[ 30x + 70y \leq 1500 \]

2. **Material (Wood) Constraint**: The artist only has enough wood to make a total of 40 items.

\[ x + y \leq 40 \]

3. **Non-Negativity Constraints**: Since the number of cutting boards and chairs cannot be negative, we have:

\[ x \geq 0 \]
\[ y \geq 0 \]

Given these constraints and our objective function, we can now formulate this problem in Gurobi code to find out how many cutting boards and chairs the artist should make to maximize his profit.

```python
from gurobipy import *

# Create a model
m = Model("Wood_Artist_Problem")

# Define decision variables
x = m.addVar(name='cutting_boards', vtype=GRB.INTEGER, lb=0)
y = m.addVar(name='chairs', vtype=GRB.INTEGER, lb=0)

# Objective function: Maximize profit
m.setObjective(14*x + 25*y, GRB.MAXIMIZE)

# Constraints
m.addConstr(30*x + 70*y <= 1500, name='time_constraint')
m.addConstr(x + y <= 40, name='material_constraint')

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found: Make {x.x} cutting boards and {y.x} chairs.")
else:
    print("No optimal solution found.")

```