## Problem Description and Formulation

The problem is a classic example of a linear programming problem. Daniel and David want to maximize their profit by producing the optimal number of batches of pancakes and bagels given the time constraints.

Let's define the decision variables:
- $x$: the number of batches of pancakes
- $y$: the number of batches of bagels

The objective function to maximize profit is:
\[ \text{Maximize:} \quad 25x + 30y \]

The constraints based on the available time for Daniel and David are:
\[ 25x + 9y \leq 150 \]
\[ 15x + 20y \leq 350 \]

Also, $x \geq 0$ and $y \geq 0$ because the number of batches cannot be negative.

## Gurobi Code

To solve this problem using Gurobi in Python, we will use the following code:

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Pancakes_and_Bagels")

# Define the decision variables
x = model.addVar(lb=0, name="Pancakes")
y = model.addVar(lb=0, name="Bagels")

# Define the objective function
model.setObjective(25*x + 30*y, gp.GRB.MAXIMIZE)

# Add the constraints
model.addConstr(25*x + 9*y <= 150, name="Daniel_Time")
model.addConstr(15*x + 20*y <= 350, name="David_Time")

# Solve the model
model.optimize()

# Check if the model is optimized
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal batches of pancakes: {x.varValue}")
    print(f"Optimal batches of bagels: {y.varValue}")
    print(f"Maximal profit: ${model.objVal:.2f}")
else:
    print("The model is infeasible.")
```

This code defines the problem in Gurobi, solves it, and prints out the optimal number of batches for pancakes and bagels, along with the maximal profit achievable. If the problem is infeasible (i.e., there are no solutions that satisfy all the constraints), it will indicate that as well.