## Step 1: Define the symbolic representation of the variables
The variables are 'lanyards', 'postage stamps', and 'cans of coffee', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to minimize is $7.8x_0 + 3.65x_1 + 4.87x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
1. $17x_0 + 6x_2 \geq 20$
2. $5x_1 + 6x_2 \geq 12$
3. $17x_0 + 5x_1 + 6x_2 \geq 20$
4. $17x_0 + 5x_1 + 6x_2 \geq 20$ (same as 3)
5. $12x_0 + 8x_2 \geq 54$
6. $11x_1 + 8x_2 \geq 52$
7. $12x_0 + 11x_1 + 8x_2 \geq 52$
8. $x_0 - 3x_1 \geq 0$
9. $17x_0 + 5x_1 + 6x_2 \leq 39$
10. $12x_0 + 8x_2 \leq 151$
11. $12x_0 + 11x_1 \leq 65$
12. $11x_1 + 8x_2 \leq 101$

## 4: Consider the bounds and integrality constraints
- $x_0, x_1, x_2$ are integers (whole numbers)
- Sustainability score upper bound: $17x_0 + 5x_1 + 6x_2 \leq 79$
- Dollar cost upper bound: $12x_0 + 11x_1 + 8x_2 \leq 163$

## 5: Formulate the symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'lanyards'), ('x1', 'postage stamps'), ('x2', 'cans of coffee')],
'objective_function': '7.8*x0 + 3.65*x1 + 4.87*x2',
'constraints': [
    '17*x0 + 6*x2 >= 20',
    '5*x1 + 6*x2 >= 12',
    '17*x0 + 5*x1 + 6*x2 >= 20',
    '12*x0 + 8*x2 >= 54',
    '11*x1 + 8*x2 >= 52',
    '12*x0 + 11*x1 + 8*x2 >= 52',
    'x0 - 3*x1 >= 0',
    '17*x0 + 5*x1 + 6*x2 <= 39',
    '12*x0 + 8*x2 <= 151',
    '12*x0 + 11*x1 <= 65',
    '11*x1 + 8*x2 <= 101',
    '17*x0 + 5*x1 + 6*x2 <= 79',
    '12*x0 + 11*x1 + 8*x2 <= 163'
]
}
```

## 6: Implement the problem using Gurobi
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="lanyards", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="postage_stamps", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="cans_of_coffee", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(7.8*x0 + 3.65*x1 + 4.87*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(17*x0 + 6*x2 >= 20)
    model.addConstr(5*x1 + 6*x2 >= 12)
    model.addConstr(17*x0 + 5*x1 + 6*x2 >= 20)
    model.addConstr(12*x0 + 8*x2 >= 54)
    model.addConstr(11*x1 + 8*x2 >= 52)
    model.addConstr(12*x0 + 11*x1 + 8*x2 >= 52)
    model.addConstr(x0 - 3*x1 >= 0)
    model.addConstr(17*x0 + 5*x1 + 6*x2 <= 39)
    model.addConstr(12*x0 + 8*x2 <= 151)
    model.addConstr(12*x0 + 11*x1 <= 65)
    model.addConstr(11*x1 + 8*x2 <= 101)
    model.addConstr(17*x0 + 5*x1 + 6*x2 <= 79)
    model.addConstr(12*x0 + 11*x1 + 8*x2 <= 163)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Lanyards: ", x0.varValue)
        print("Postage Stamps: ", x1.varValue)
        print("Cans of Coffee: ", x2.varValue)
    else:
        print("No optimal solution found")

solve_optimization_problem()
```