## Step 1: Define the symbolic representation of the variables
The variables are 'corn cobs', 'lemons', 'oranges', and 'hot dogs', which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $8x_0 + 8x_1 + 7x_2 + 5x_3$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $15x_0 + 13x_1 + 15x_2 + 9x_3 \leq 205$ (fiber)
- $11x_0 + 15x_1 + 11x_2 + 16x_3 \leq 162$ (tastiness rating)
- $7x_0 + 2x_1 + 3x_2 + 12x_3 \leq 205$ (fat)
- $15x_2 + 9x_3 \geq 48$ (fiber from oranges and hot dogs)
- $15x_0 + 13x_1 \geq 49$ (fiber from corn cobs and lemons)
- $15x_0 + 9x_3 \geq 37$ (fiber from corn cobs and hot dogs)
- $13x_1 + 9x_3 \geq 43$ (fiber from lemons and hot dogs)
- $15x_0 + 13x_1 + 15x_2 + 9x_3 \geq 43$ (total fiber)
- $11x_0 + 11x_2 \geq 25$ (tastiness from corn cobs and oranges)
- $11x_0 + 15x_1 \geq 40$ (tastiness from corn cobs and lemons)
- $11x_0 + 15x_1 + 11x_2 + 16x_3 \geq 40$ (total tastiness)
- $2x_1 + 3x_2 \geq 26$ (fat from lemons and oranges)
- $7x_0 + 12x_3 \geq 37$ (fat from corn cobs and hot dogs)
- $7x_0 + 2x_1 \geq 32$ (fat from corn cobs and lemons)
- $7x_0 + 2x_1 + 3x_2 + 12x_3 \geq 32$ (total fat)
- $8x_0 - 10x_1 \geq 0$
- $-6x_1 + 2x_3 \geq 0$
- $13x_1 + 15x_2 + 9x_3 \leq 149$ (fiber from lemons, oranges, and hot dogs)
- $15x_0 + 13x_1 + 9x_3 \leq 105$ (fiber from corn cobs, lemons, and hot dogs)
- $11x_0 + 11x_2 \leq 129$ (tastiness from corn cobs and oranges)
- $15x_1 + 11x_2 \leq 131$ (tastiness from lemons and oranges)
- $15x_1 + 16x_3 \leq 104$ (tastiness from lemons and hot dogs)
- $11x_0 + 16x_3 \leq 121$ (tastiness from corn cobs and hot dogs)
- $7x_0 + 2x_1 + 3x_2 \leq 152$ (fat from corn cobs, lemons, and oranges)

## Step 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'corn cobs'),
        ('x1', 'lemons'),
        ('x2', 'oranges'),
        ('x3', 'hot dogs')
    ],
    'objective_function': '8*x0 + 8*x1 + 7*x2 + 5*x3',
    'constraints': [
        '15*x0 + 13*x1 + 15*x2 + 9*x3 <= 205',
        '11*x0 + 15*x1 + 11*x2 + 16*x3 <= 162',
        '7*x0 + 2*x1 + 3*x2 + 12*x3 <= 205',
        '15*x2 + 9*x3 >= 48',
        '15*x0 + 13*x1 >= 49',
        '15*x0 + 9*x3 >= 37',
        '13*x1 + 9*x3 >= 43',
        '15*x0 + 13*x1 + 15*x2 + 9*x3 >= 43',
        '11*x0 + 11*x2 >= 25',
        '11*x0 + 15*x1 >= 40',
        '11*x0 + 15*x1 + 11*x2 + 16*x3 >= 40',
        '2*x1 + 3*x2 >= 26',
        '7*x0 + 12*x3 >= 37',
        '7*x0 + 2*x1 >= 32',
        '7*x0 + 2*x1 + 3*x2 + 12*x3 >= 32',
        '8*x0 - 10*x1 >= 0',
        '-6*x1 + 2*x3 >= 0',
        '13*x1 + 15*x2 + 9*x3 <= 149',
        '15*x0 + 13*x1 + 9*x3 <= 105',
        '11*x0 + 11*x2 <= 129',
        '15*x1 + 11*x2 <= 131',
        '15*x1 + 16*x3 <= 104',
        '11*x0 + 16*x3 <= 121',
        '7*x0 + 2*x1 + 3*x2 <= 152'
    ]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name='corn_cobs', lb=0)
x1 = m.addVar(name='lemons', lb=0)
x2 = m.addVar(name='oranges', lb=0)
x3 = m.addVar(name='hot_dogs', lb=0)

# Set the objective function
m.setObjective(8*x0 + 8*x1 + 7*x2 + 5*x3, gurobi.GRB.MINIMIZE)

# Add constraints
m.addConstr(15*x0 + 13*x1 + 15*x2 + 9*x3 <= 205)
m.addConstr(11*x0 + 15*x1 + 11*x2 + 16*x3 <= 162)
m.addConstr(7*x0 + 2*x1 + 3*x2 + 12*x3 <= 205)
m.addConstr(15*x2 + 9*x3 >= 48)
m.addConstr(15*x0 + 13*x1 >= 49)
m.addConstr(15*x0 + 9*x3 >= 37)
m.addConstr(13*x1 + 9*x3 >= 43)
m.addConstr(15*x0 + 13*x1 + 15*x2 + 9*x3 >= 43)
m.addConstr(11*x0 + 11*x2 >= 25)
m.addConstr(11*x0 + 15*x1 >= 40)
m.addConstr(11*x0 + 15*x1 + 11*x2 + 16*x3 >= 40)
m.addConstr(2*x1 + 3*x2 >= 26)
m.addConstr(7*x0 + 12*x3 >= 37)
m.addConstr(7*x0 + 2*x1 >= 32)
m.addConstr(7*x0 + 2*x1 + 3*x2 + 12*x3 >= 32)
m.addConstr(8*x0 - 10*x1 >= 0)
m.addConstr(-6*x1 + 2*x3 >= 0)
m.addConstr(13*x1 + 15*x2 + 9*x3 <= 149)
m.addConstr(15*x0 + 13*x1 + 9*x3 <= 105)
m.addConstr(11*x0 + 11*x2 <= 129)
m.addConstr(15*x1 + 11*x2 <= 131)
m.addConstr(15*x1 + 16*x3 <= 104)
m.addConstr(11*x0 + 16*x3 <= 121)
m.addConstr(7*x0 + 2*x1 + 3*x2 <= 152)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objval)
    print('corn cobs: ', x0.varValue)
    print('lemons: ', x1.varValue)
    print('oranges: ', x2.varValue)
    print('hot dogs: ', x3.varValue)
else:
    print('No solution found')
```