To solve Mark's problem, we need to determine the optimal number of chewable and regular pills he should buy to meet his daily vitamin requirements at minimum cost. We can model this as a linear programming problem.

Let's define two decision variables:
- $x$: The number of chewable pills Mark buys.
- $y$: The number of regular pills Mark buys.

The objective function is to minimize the total cost, which is given by $0.50x + 0.40y$ since each chewable pill costs $0.50 and each regular pill costs $0.40.

We have four constraints based on the vitamin requirements:
1. Vitamin A: $2x + 3y \geq 30$
2. Vitamin C: $3x + 2y \geq 20$
3. Vitamin D: $3x + 4y \geq 40$
4. Vitamin E: $2x + 4y \geq 30$

Additionally, $x$ and $y$ must be non-negative since Mark cannot buy a negative number of pills.

Now, let's translate this into Gurobi code in Python:

```python
from gurobipy import *

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

# Define the decision variables
x = m.addVar(vtype=GRB.CONTINUOUS, name="chewable_pills", lb=0)
y = m.addVar(vtype=GRB.CONTINUOUS, name="regular_pills", lb=0)

# Define the objective function
m.setObjective(0.50*x + 0.40*y, GRB.MINIMIZE)

# Add the constraints
m.addConstr(2*x + 3*y >= 30, "Vitamin_A")
m.addConstr(3*x + 2*y >= 20, "Vitamin_C")
m.addConstr(3*x + 4*y >= 40, "Vitamin_D")
m.addConstr(2*x + 4*y >= 30, "Vitamin_E")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Chewable pills: {x.x}")
    print(f"Regular pills: {y.x}")
    print(f"Total cost: ${0.50*x.x + 0.40*y.x:.2f}")
else:
    print("No optimal solution found")
```