## Step 1: Define the symbolic representation of the problem
The problem involves finding the optimal number of blue and red gummies a patient should purchase to minimize cost while meeting certain nutritional requirements. Let's define the symbolic variables:
- $x_1$ represents the number of blue gummies
- $x_2$ represents the number of red gummies

The objective is to minimize the total cost, which is $2x_1 + 3x_2$.

## Step 2: Define the constraints based on nutritional requirements
The patient must get at least:
- 40 units of calcium: $3x_1 + 4x_2 \geq 40$
- 45 units of vitamin A: $2x_1 + 3x_2 \geq 45$
- 20 units of iron: $5x_1 + 2x_2 \geq 20$

Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of gummies cannot be negative.

## 3: Symbolic representation in JSON format
```json
{
'sym_variables': [('x1', 'blue gummies'), ('x2', 'red gummies')],
'objective_function': '2*x1 + 3*x2',
'constraints': [
    '3*x1 + 4*x2 >= 40',
    '2*x1 + 3*x2 >= 45',
    '5*x1 + 2*x2 >= 20',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 4: Convert the problem into Gurobi code in Python
```python
import gurobipy as gp

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

# Define the variables
x1 = m.addVar(name="blue_gummies", lb=0, vtype=gp.GRB.INTEGER)  # Number of blue gummies
x2 = m.addVar(name="red_gummies", lb=0, vtype=gp.GRB.INTEGER)  # Number of red gummies

# Define the objective function
m.setObjective(2*x1 + 3*x2, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(3*x1 + 4*x2 >= 40, name="calcium_requirement")
m.addConstr(2*x1 + 3*x2 >= 45, name="vitamin_A_requirement")
m.addConstr(5*x1 + 2*x2 >= 20, name="iron_requirement")

# Solve the model
m.optimize()

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