To solve the optimization problem described, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the given information.

Let's denote:
- $x_1$ as the number of units of cherry tomatoes used.
- $x_2$ as the number of units of cocktail tomatoes used.

The objective is to minimize the cost of producing the tomato paste. The cost can be represented by the objective function:
\[3x_1 + 4x_2\]

Given the requirements for sugar and acid content, we have two constraints:
1. Sugar constraint: $5x_1 + 2.5x_2 \geq 350$
2. Acid constraint: $1.5x_1 + 3x_2 \geq 250$

Additionally, since we cannot use negative units of tomatoes, we have non-negativity constraints:
- $x_1 \geq 0$
- $x_2 \geq 0$

The symbolic representation of the problem can be summarized as follows:

```json
{
    'sym_variables': [('x1', 'number of units of cherry tomatoes'), ('x2', 'number of units of cocktail tomatoes')],
    'objective_function': '3*x1 + 4*x2',
    'constraints': [
        '5*x1 + 2.5*x2 >= 350',
        '1.5*x1 + 3*x2 >= 250',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(lb=0, name="cherry_tomatoes")
x2 = m.addVar(lb=0, name="cocktail_tomatoes")

# Set the objective function
m.setObjective(3*x1 + 4*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(5*x1 + 2.5*x2 >= 350, "sugar_constraint")
m.addConstr(1.5*x1 + 3*x2 >= 250, "acid_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Cherry tomatoes: {x1.x}")
    print(f"Cocktail tomatoes: {x2.x}")
    print(f"Minimum cost: {m.objVal}")
else:
    print("No optimal solution found")
```