## Step 1: Define the symbolic representation of the variables
The variables are 'ham sandwiches', 'rotisserie chickens', and 'peanutbutter sandwiches', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_0$ : ham sandwiches
- $x_1$ : rotisserie chickens
- $x_2$ : peanutbutter sandwiches

## Step 3: Define the objective function in symbolic notation
The objective function to minimize is $1.84x_0 + 1.46x_1 + 8.82x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $3.95x_0 + 1.0x_2 \geq 20$ (at least 20 milligrams of iron from ham sandwiches and peanutbutter sandwiches)
- $3.95x_0 + 0.36x_1 + 1.0x_2 \geq 20$ (at least 20 milligrams of iron from all sources)
- $5.08x_0 + 0.37x_2 \geq 63$ (umami index from ham sandwiches and peanutbutter sandwiches)
- $5.67x_1 + 0.37x_2 \geq 61$ (umami index from rotisserie chickens and peanutbutter sandwiches)
- $5.08x_0 + 5.67x_1 + 0.37x_2 \geq 69$ (umami index from all sources)
- $-10x_1 + 8x_2 \geq 0$ (rotisserie chickens and peanutbutter sandwiches constraint)

## 5: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'ham sandwiches'), 
        ('x1', 'rotisserie chickens'), 
        ('x2', 'peanutbutter sandwiches')
    ], 
    'objective_function': '1.84*x0 + 1.46*x1 + 8.82*x2', 
    'constraints': [
        '3.95*x0 + 1.0*x2 >= 20', 
        '3.95*x0 + 0.36*x1 + 1.0*x2 >= 20', 
        '5.08*x0 + 0.37*x2 >= 63', 
        '5.67*x1 + 0.37*x2 >= 61', 
        '5.08*x0 + 5.67*x1 + 0.37*x2 >= 69', 
        '-10*x1 + 8*x2 >= 0'
    ]
}
```

## 6: Write the Gurobi code to solve the optimization problem
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x0 = model.addVar(name="ham_sandwiches", lb=0)  # ham sandwiches
    x1 = model.addVar(name="rotisserie_chickens", lb=0)  # rotisserie chickens
    x2 = model.addVar(name="peanutbutter_sandwiches", lb=0)  # peanutbutter sandwiches

    # Define the objective function
    model.setObjective(1.84 * x0 + 1.46 * x1 + 8.82 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(3.95 * x0 + 1.0 * x2 >= 20)  # at least 20 milligrams of iron from ham sandwiches and peanutbutter sandwiches
    model.addConstr(3.95 * x0 + 0.36 * x1 + 1.0 * x2 >= 20)  # at least 20 milligrams of iron from all sources
    model.addConstr(5.08 * x0 + 0.37 * x2 >= 63)  # umami index from ham sandwiches and peanutbutter sandwiches
    model.addConstr(5.67 * x1 + 0.37 * x2 >= 61)  # umami index from rotisserie chickens and peanutbutter sandwiches
    model.addConstr(5.08 * x0 + 5.67 * x1 + 0.37 * x2 >= 69)  # umami index from all sources
    model.addConstr(-10 * x1 + 8 * x2 >= 0)  # rotisserie chickens and peanutbutter sandwiches constraint

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Ham sandwiches: {x0.varValue}")
        print(f"Rotisserie chickens: {x1.varValue}")
        print(f"Peanutbutter sandwiches: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```