To solve this optimization problem, we need to define the decision variables, objective function, and constraints.

Let's denote:
- $L$ as the number of large artworks made,
- $S$ as the number of small artworks made.

The objective is to maximize profit. Given that the profit per large artwork is $200 and per small artwork is $75, our objective function can be written as:
\[ \text{Maximize} \quad 200L + 75S \]

We have several constraints based on the available resources (paint, glitter, glue) and the minimum production requirements for both types of artworks.

1. **Paint constraint**: Each large artwork requires 5 units of paint, and each small artwork requires 3 units of paint. The store has 200 units of paint available.
\[ 5L + 3S \leq 200 \]

2. **Glitter constraint**: Each large artwork requires 3 units of glitter, and each small artwork requires 1 unit of glitter. The store has 100 units of glitter available.
\[ 3L + S \leq 100 \]

3. **Glue constraint**: Each large artwork requires 4 units of glue, and each small artwork requires 2 units of glue. The store has 80 units of glue available.
\[ 4L + 2S \leq 80 \]

4. **Minimum production constraints**:
   - For large artworks: $L \geq 5$
   - For small artworks: $S \geq 10$

Now, let's write the Gurobi code to solve this linear programming problem:

```python
from gurobipy import *

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

# Decision variables
L = m.addVar(vtype=GRB.CONTINUOUS, name="Large_Artworks")
S = m.addVar(vtype=GRB.CONTINUOUS, name="Small_Artworks")

# Objective function: Maximize profit
m.setObjective(200*L + 75*S, GRB.MAXIMIZE)

# Constraints
m.addConstr(5*L + 3*S <= 200, "Paint_Constraint")
m.addConstr(3*L + S <= 100, "Glitter_Constraint")
m.addConstr(4*L + 2*S <= 80, "Glue_Constraint")
m.addConstr(L >= 5, "Min_Large_Artworks")
m.addConstr(S >= 10, "Min_Small_Artworks")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Large Artworks: {L.x}")
    print(f"Small Artworks: {S.x}")
    print(f"Maximum Profit: {m.objVal}")
else:
    print("No optimal solution found")
```