## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of large artworks
- $x_2$ represents the number of small artworks

## Step 2: Formulate the objective function
The objective function is to maximize profit. The profit per large artwork is $200, and the profit per small artwork is $75. Therefore, the objective function can be written as:
Maximize $200x_1 + 75x_2$

## 3: Define the constraints
The store has limited resources:
- 200 units of paint
- 100 units of glitter
- 80 units of glue
And there are requirements for the minimum number of artworks:
- At least 5 units of large artworks
- At least 10 units of small artworks

The constraints based on the resources are:
- $5x_1 + 3x_2 \leq 200$ (paint constraint)
- $3x_1 + x_2 \leq 100$ (glitter constraint)
- $4x_1 + 2x_2 \leq 80$ (glue constraint)

The constraints based on the minimum requirements are:
- $x_1 \geq 5$ (large artworks constraint)
- $x_2 \geq 10$ (small artworks constraint)

## 4: Non-negativity constraints
Both $x_1$ and $x_2$ must be non-negative since they represent the number of artworks:
- $x_1 \geq 0$
- $x_2 \geq 0$

However, given the constraints $x_1 \geq 5$ and $x_2 \geq 10$, the non-negativity constraints are implicitly satisfied.

## 5: Symbolic Representation
The symbolic representation of the problem is:
```json
{
'sym_variables': [('x1', 'large artworks'), ('x2', 'small artworks')],
'objective_function': '200*x1 + 75*x2',
'constraints': [
    '5*x1 + 3*x2 <= 200',
    '3*x1 + x2 <= 100',
    '4*x1 + 2*x2 <= 80',
    'x1 >= 5',
    'x2 >= 10'
]
}
```

## 6: Gurobi Code
Now, let's implement this problem using Gurobi in Python:
```python
import gurobi

def solve_artwork_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(lb=5, name="large_artworks")  # At least 5 large artworks
    x2 = model.addVar(lb=10, name="small_artworks")  # At least 10 small artworks

    # Objective function: Maximize 200*x1 + 75*x2
    model.setObjective(200*x1 + 75*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(5*x1 + 3*x2 <= 200, name="paint_constraint")
    model.addConstr(3*x1 + x2 <= 100, name="glitter_constraint")
    model.addConstr(4*x1 + 2*x2 <= 80, name="glue_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of large artworks: {x1.varValue}")
        print(f"Number of small artworks: {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_artwork_problem()
```