## Step 1: Define the symbolic representation of the problem

Let's denote:
- $x_1$ as the hours the university cafe is run
- $x_2$ as the hours the downtown cafe is run

The objective is to minimize the total cost, which can be represented as $400x_1 + 700x_2$.

The constraints based on the production requirements are:
- $30x_1 + 40x_2 \geq 900$ (cappuccinos)
- $40x_1 + 70x_2 \geq 700$ (lattes)
- $60x_1 + 110x_2 \geq 1400$ (regular coffees)
- $x_1 \geq 0$ and $x_2 \geq 0$ (non-negativity constraints)

## Step 2: Convert the problem into a Gurobi-compatible format

The symbolic representation can be directly translated into Gurobi code. We will use the Gurobi Python API to model and solve this linear programming problem.

## 3: Write the Gurobi code

```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="university_cafe_hours", lb=0)
x2 = model.addVar(name="downtown_cafe_hours", lb=0)

# Objective function: minimize 400x1 + 700x2
model.setObjective(400 * x1 + 700 * x2, gurobi.GRB.MINIMIZE)

# Constraints
model.addConstr(30 * x1 + 40 * x2 >= 900, name="cappuccino_constraint")
model.addConstr(40 * x1 + 70 * x2 >= 700, name="latte_constraint")
model.addConstr(60 * x1 + 110 * x2 >= 1400, name="regular_coffee_constraint")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"University cafe hours: {x1.varValue}")
    print(f"Downtown cafe hours: {x2.varValue}")
    print(f"Total cost: {model.objVal}")
else:
    print("No optimal solution found.")
```

## 4: Provide the symbolic representation in JSON format

```json
{
  "sym_variables": [
    ["x1", "university cafe hours"],
    ["x2", "downtown cafe hours"]
  ],
  "objective_function": "400x1 + 700x2",
  "constraints": [
    "30x1 + 40x2 >= 900",
    "40x1 + 70x2 >= 700",
    "60x1 + 110x2 >= 1400",
    "x1 >= 0",
    "x2 >= 0"
  ]
}
```