To solve this optimization problem, we first need to define the decision variables and the objective function. Let's denote the number of paintings as \(P\) and the number of photo prints as \(Ph\). The objective is to maximize profit, which is calculated as the profit per painting times the number of paintings plus the profit per photo print times the number of photo prints: \(330P + 170Ph\).

We have two main constraints:
1. **Wall Space Constraint**: Each painting takes 7 sq ft of wall space, and each photo print takes 4 sq ft. The total available wall space is 200 sq ft. This can be represented as \(7P + 4Ph \leq 200\).
2. **Budget Constraint**: The cost of a painting is $400, and the cost of a photo print is $200. The gallery has a budget of $7000. This constraint can be written as \(400P + 200Ph \leq 7000\).

Additionally, we have a constraint that at least 20% of the items in stock must be photo prints. If \(T = P + Ph\) represents the total number of items, then this constraint is \(Ph \geq 0.20T\) or \(Ph \geq 0.20(P + Ph)\), which simplifies to \(Ph \geq 0.20P + 0.20Ph\), and further to \(0.80Ph \geq 0.20P\).

Given these constraints, we aim to find the values of \(P\) and \(Ph\) that maximize profit.

```python
from gurobipy import *

# Create a new model
m = Model("Art Gallery Optimization")

# Decision variables
P = m.addVar(vtype=GRB.INTEGER, name="Paintings")
Ph = m.addVar(vtype=GRB.INTEGER, name="PhotoPrints")

# Objective function: Maximize profit
m.setObjective(330*P + 170*Ph, GRB.MAXIMIZE)

# Constraints
# Wall space constraint
m.addConstr(7*P + 4*Ph <= 200, "WallSpace")
# Budget constraint
m.addConstr(400*P + 200*Ph <= 7000, "Budget")
# At least 20% of items are photo prints
m.addConstr(0.80*Ph >= 0.20*P, "PhotoPrintPercentage")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of Paintings: {P.x}")
    print(f"Number of Photo Prints: {Ph.x}")
    print(f"Maximum Profit: {m.objVal}")
else:
    print("No optimal solution found")
```