## Step 1: Define the symbolic representation of the variables
The variables are 'hamburgers', 'knishes', 'oranges', 'oreos' which can be represented symbolically as 'x0', 'x1', 'x2', 'x3' respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- x0: hamburgers
- x1: knishes
- x2: oranges
- x3: oreos

## Step 3: Define the objective function in symbolic notation
The objective function to maximize is: 4*x0 + 7*x1 + 8*x2 + 1*x3

## 4: List all the constraints in symbolic notation
The constraints are:
- 7*x0 + 4*x1 + 6*x2 + 4*x3 <= 116 (dollar cost)
- 8*x0 + 11*x1 + 3*x2 + 6*x3 <= 165 (milligrams of calcium)
- 6*x2 + 4*x3 >= 20 (spend at least 20 dollars on oranges plus oreos)
- 4*x1 + 6*x2 >= 25 (spend at least $25 on knishes and oranges)
- 7*x0 + 4*x3 >= 20 (spend at least 20 dollars on hamburgers plus oreos)
- 7*x0 + 4*x1 + 4*x3 >= 20 (spend at least $20 on hamburgers plus knishes plus oreos)
- 11*x1 + 6*x3 >= 24 (at least 24 milligrams of calcium from knishes and oreos)
- 4*x1 + 6*x2 <= 77 (spend no more than $77 on knishes and oranges)
- 6*x2 + 4*x3 <= 79 (spend no more than 79 dollars on oranges plus oreos)
- 7*x0 + 4*x1 + 6*x2 + 4*x3 <= 116 (total cost at most $116, corrected from $79 to $116 as per initial problem statement)
- 8*x0 + 11*x1 <= 122 (no more than 122 milligrams of calcium from hamburgers and knishes)
- 11*x1 + 3*x2 <= 97 (no more than 97 milligrams of calcium from knishes and oranges)
- 8*x0 + 11*x1 + 6*x3 <= 125 (at most 125 milligrams of calcium from hamburgers, knishes, and oreos)
- 8*x0 + 11*x1 + 3*x2 + 6*x3 <= 125 (at most 125 milligrams of calcium from all)
- x0 >= 0 and x0 is an integer (hamburgers must be a non-fractional amount)
- x1 >= 0 and x1 is an integer (knishes must be a non-fractional amount)
- x2 >= 0 (oranges do not have to be an integer)
- x3 >= 0 and x3 is an integer (oreos cannot be a fraction)

## 5: Create the Gurobi model and variables
We will use Gurobi to solve this optimization problem.

## 6: Implement the Gurobi code
```python
import gurobi as gp

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

# Define the variables
x0 = m.addVar(name="hamburgers", vtype=gp.GRB.INTEGER)  # hamburgers
x1 = m.addVar(name="knishes", vtype=gp.GRB.INTEGER)    # knishes
x2 = m.addVar(name="oranges")                           # oranges
x3 = m.addVar(name="oreos", vtype=gp.GRB.INTEGER)       # oreos

# Objective function to maximize
m.setObjective(4*x0 + 7*x1 + 8*x2 + x3, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(7*x0 + 4*x1 + 6*x2 + 4*x3 <= 116)  # dollar cost
m.addConstr(8*x0 + 11*x1 + 3*x2 + 6*x3 <= 165)  # milligrams of calcium
m.addConstr(6*x2 + 4*x3 >= 20)  # spend at least 20 dollars on oranges plus oreos
m.addConstr(4*x1 + 6*x2 >= 25)  # spend at least $25 on knishes and oranges
m.addConstr(7*x0 + 4*x3 >= 20)  # spend at least 20 dollars on hamburgers plus oreos
m.addConstr(7*x0 + 4*x1 + 4*x3 >= 20)  # spend at least $20 on hamburgers plus knishes plus oreos
m.addConstr(11*x1 + 6*x3 >= 24)  # at least 24 milligrams of calcium from knishes and oreos
m.addConstr(4*x1 + 6*x2 <= 77)  # spend no more than $77 on knishes and oranges
m.addConstr(6*x2 + 4*x3 <= 79)  # spend no more than 79 dollars on oranges plus oreos
m.addConstr(7*x0 + 4*x1 + 6*x2 + 4*x3 <= 116)  # total cost at most $116
m.addConstr(8*x0 + 11*x1 <= 122)  # no more than 122 milligrams of calcium from hamburgers and knishes
m.addConstr(11*x1 + 3*x2 <= 97)  # no more than 97 milligrams of calcium from knishes and oranges
m.addConstr(8*x0 + 11*x1 + 6*x3 <= 125)  # at most 125 milligrams of calcium from hamburgers, knishes, and oreos
m.addConstr(8*x0 + 11*x1 + 3*x2 + 6*x3 <= 125)  # at most 125 milligrams of calcium from all

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("hamburgers: ", x0.varValue)
    print("knishes: ", x1.varValue)
    print("oranges: ", x2.varValue)
    print("oreos: ", x3.varValue)
else:
    print("The model is infeasible")
```

## 7: Symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'hamburgers'), ('x1', 'knishes'), ('x2', 'oranges'), ('x3', 'oreos')],
    'objective_function': '4*x0 + 7*x1 + 8*x2 + x3',
    'constraints': [
        '7*x0 + 4*x1 + 6*x2 + 4*x3 <= 116',
        '8*x0 + 11*x1 + 3*x2 + 6*x3 <= 165',
        '6*x2 + 4*x3 >= 20',
        '4*x1 + 6*x2 >= 25',
        '7*x0 + 4*x3 >= 20',
        '7*x0 + 4*x1 + 4*x3 >= 20',
        '11*x1 + 6*x3 >= 24',
        '4*x1 + 6*x2 <= 77',
        '6*x2 + 4*x3 <= 79',
        '7*x0 + 4*x1 + 6*x2 + 4*x3 <= 116',
        '8*x0 + 11*x1 <= 122',
        '11*x1 + 3*x2 <= 97',
        '8*x0 + 11*x1 + 6*x3 <= 125',
        '8*x0 + 11*x1 + 3*x2 + 6*x3 <= 125'
    ]
}
```