To solve the optimization problem described, we will use the Gurobi Python interface to formulate and solve the linear program. The problem involves minimizing an objective function subject to several constraints related to nutritional content (calcium) and taste (sourness index) of two food items: bagged salads and potatoes.

Given:
- Objective Function: Minimize \(1 \times \text{bagged salads} + 4 \times \text{potatoes}\)
- Constraints:
  - Calcium content constraints
    - Lower bound: \(39\) mg (at least)
    - Upper bound: \(100\) mg (at most)
  - Sourness index constraints
    - Lower bound: \(59\)
    - Upper bound: \(80\)
  - Additional constraint: \(-5 \times \text{bagged salads} + 8 \times \text{potatoes} \geq 0\)

Formulation:
Let \(x_0\) be the amount of bagged salads and \(x_1\) be the amount of potatoes.

- Objective Function: Minimize \(x_0 + 4x_1\)
- Constraints:
  - Calcium: \(4.0x_0 + 0.84x_1 \geq 39\) (at least 39 mg) and \(4.0x_0 + 0.84x_1 \leq 100\) (no more than 100 mg)
  - Sourness Index: \(12.96x_0 + 15.92x_1 \geq 59\) (at least 59) and \(12.96x_0 + 15.92x_1 \leq 80\) (no more than 80)
  - Additional Constraint: \(-5x_0 + 8x_1 \geq 0\)

All variables are continuous, meaning they can take any fractional value.

```python
from gurobipy import *

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

# Define the variables
bagged_salads = m.addVar(vtype=GRB.CONTINUOUS, name="bagged_salads")
potatoes = m.addVar(vtype=GRB.CONTINUOUS, name="potatoes")

# Set the objective function
m.setObjective(bagged_salads + 4 * potatoes, GRB.MINIMIZE)

# Add constraints
m.addConstr(4.0 * bagged_salads + 0.84 * potatoes >= 39, "Calcium_Lower_Bound")
m.addConstr(4.0 * bagged_salads + 0.84 * potatoes <= 100, "Calcium_Upper_Bound")
m.addConstr(12.96 * bagged_salads + 15.92 * potatoes >= 59, "Sourness_Lower_Bound")
m.addConstr(12.96 * bagged_salads + 15.92 * potatoes <= 80, "Sourness_Upper_Bound")
m.addConstr(-5 * bagged_salads + 8 * potatoes >= 0, "Additional_Constraint")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: {bagged_salads.varName} = {bagged_salads.x}, {potatoes.varName} = {potatoes.x}")
else:
    print("No optimal solution found")
```