## Step 1: Define the symbolic representation of the problem
The symbolic representation of the problem consists of pairs of variables in symbolic notation and their corresponding natural language objects, the objective function rendered as an algebraic term, and the list of semi-algebraic constraints.

## Step 2: Identify the variables and their corresponding symbolic notation
Let's denote the variables as follows:
- 'postage stamps': 'x0'
- 'manila envelopes': 'x1'
- '3D printers': 'x2'
- 'packs of paper': 'x3'
- 'lanyards': 'x4'
- 'paper clips': 'x5'
- 'red pens': 'x6'
- 'color printers': 'x7'

## Step 3: Formulate the objective function
The objective function to maximize is: 
8*x0 + 7*x1 + 5*x2 + 5*x3 + 9*x4 + 8*x5 + 2*x6 + 1*x7

## Step 4: List the constraints
Constraints:
- Usefulness rating constraints:
  - 13*x0 <= 296
  - 7*x1 <= 296
  - 1*x2 <= 296
  - 6*x3 <= 296
  - 8*x4 <= 296
  - 8*x5 <= 296
  - 11*x6 <= 296
  - 6*x7 <= 296
- Weight constraints:
  - 5*x0 <= 214
  - 2*x1 <= 214
  - 6*x2 <= 214
  - 3*x3 <= 214
  - 5*x4 <= 214
  - 2*x5 <= 214
  - 9*x6 <= 214
  - 11*x7 <= 214
- Other constraints:
  - 13*x0 + 1*x2 >= 16
  - 7*x1 + 8*x5 >= 19
  - 8*x4 + 11*x6 >= 18
  - 13*x0 + 8*x4 >= 17
  - 7*x1 + 6*x3 >= 19
  - 6*x3 + 8*x4 >= 21
  - 6*x3 + 8*x5 >= 18
  - 8*x5 + 6*x7 >= 13
  - 7*x1 + 6*x3 + 8*x4 >= 24
  - 13*x0 + 1*x2 + 8*x5 >= 24
  - 13*x0 + 7*x1 + 11*x6 >= 24
  - 7*x1 + 8*x5 + 6*x7 >= 24
  - 6*x3 + 8*x4 + 6*x7 >= 24
  - 8*x4 + 11*x6 + 6*x7 >= 24
  - 1*x2 + 8*x5 + 11*x6 >= 24
  - 7*x1 + 1*x2 + 6*x3 >= 24
  - 7*x1 + 1*x2 + 6*x7 >= 24
  - 13*x0 + 1*x2 + 6*x7 >= 24
  - 6*x3 + 8*x5 + 8*x7 >= 24
  - 1*x2 + 6*x3 + 8*x5 >= 24
  - 13*x0 + 8*x5 + 6*x7 >= 24
  - 13*x0 + 6*x3 + 8*x4 >= 24
  - 13*x0 + 7*x1 + 8*x4 >= 24
  - 7*x1 + 8*x4 + 6*x7 >= 24
  - 7*x1 + 6*x3 + 8*x4 >= 22
  - 13*x0 + 1*x2 + 8*x5 >= 22
  - 13*x0 + 7*x1 + 11*x6 >= 22
  - 7*x1 + 8*x5 + 6*x7 >= 22
  - 6*x3 + 8*x4 + 6*x7 >= 22
  - 8*x4 + 11*x6 + 6*x7 >= 22
  - 1*x2 + 8*x5 + 11*x6 >= 22
  - 7*x1 + 1*x2 + 6*x3 >= 22
  - 7*x1 + 1*x2 + 6*x7 >= 22
  - 13*x0 + 1*x2 + 6*x7 >= 22
  - 6*x3 + 8*x5 + 8*x7 >= 22
  - 1*x2 + 6*x3 + 8*x5 >= 22
  - 13*x0 + 8*x5 + 6*x7 >= 22
  - 13*x0 + 6*x3 + 8*x4 >= 22
  - 13*x0 + 7*x1 + 8*x4 >= 22
  - 7*x1 + 8*x4 + 6*x7 >= 22
- Weight constraints continued:
  - x0, x1, x2, x3, x4, x5, x6, x7 are integers
  - x0 >= 0
  - x1 >= 0
  - x2 >= 0
  - x3 >= 0
  - x4 >= 0
  - x5 >= 0
  - x6 >= 0
  - x7 >= 0

## Step 5: Provide the symbolic representation in JSON format
```json
{
  "sym_variables": [
    ["x0", "postage stamps"],
    ["x1", "manila envelopes"],
    ["x2", "3D printers"],
    ["x3", "packs of paper"],
    ["x4", "lanyards"],
    ["x5", "paper clips"],
    ["x6", "red pens"],
    ["x7", "color printers"]
  ],
  "objective_function": "8*x0 + 7*x1 + 5*x2 + 5*x3 + 9*x4 + 8*x5 + 2*x6 + 1*x7",
  "constraints": [
    "13*x0 <= 296",
    "7*x1 <= 296",
    "1*x2 <= 296",
    "6*x3 <= 296",
    "8*x4 <= 296",
    "8*x5 <= 296",
    "11*x6 <= 296",
    "6*x7 <= 296",
    "5*x0 <= 214",
    "2*x1 <= 214",
    "6*x2 <= 214",
    "3*x3 <= 214",
    "5*x4 <= 214",
    "2*x5 <= 214",
    "9*x6 <= 214",
    "11*x7 <= 214",
    "13*x0 + 1*x2 >= 16",
    "7*x1 + 8*x5 >= 19",
    "8*x4 + 11*x6 >= 18",
    "13*x0 + 8*x4 >= 17",
    "7*x1 + 6*x3 >= 19",
    "6*x3 + 8*x4 >= 21",
    "6*x3 + 8*x5 >= 18",
    "8*x5 + 6*x7 >= 13",
    "7*x1 + 6*x3 + 8*x4 >= 24",
    "13*x0 + 1*x2 + 8*x5 >= 24",
    "13*x0 + 7*x1 + 11*x6 >= 24",
    "7*x1 + 8*x5 + 6*x7 >= 24",
    "6*x3 + 8*x4 + 6*x7 >= 24",
    "8*x4 + 11*x6 + 6*x7 >= 24",
    "1*x2 + 8*x5 + 11*x6 >= 24",
    "7*x1 + 1*x2 + 6*x3 >= 24",
    "7*x1 + 1*x2 + 6*x7 >= 24",
    "13*x0 + 1*x2 + 6*x7 >= 24",
    "6*x3 + 8*x5 + 8*x7 >= 24",
    "1*x2 + 6*x3 + 8*x5 >= 24",
    "13*x0 + 8*x5 + 6*x7 >= 24",
    "13*x0 + 6*x3 + 8*x4 >= 24",
    "13*x0 + 7*x1 + 8*x4 >= 24",
    "7*x1 + 8*x4 + 6*x7 >= 24",
    "x0, x1, x2, x3, x4, x5, x6, x7 >= 0 and are integers"
  ]
}
```

## Step 6: Write the Gurobi code
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="postage_stamps", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="manila_envelopes", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="3D_printers", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="packs_of_paper", vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name="lanyards", vtype=gurobi.GRB.INTEGER)
    x5 = model.addVar(name="paper_clips", vtype=gurobi.GRB.INTEGER)
    x6 = model.addVar(name="red_pens", vtype=gurobi.GRB.INTEGER)
    x7 = model.addVar(name="color_printers", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(8*x0 + 7*x1 + 5*x2 + 5*x3 + 9*x4 + 8*x5 + 2*x6 + 1*x7, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(13*x0 <= 296)
    model.addConstr(7*x1 <= 296)
    model.addConstr(x2 <= 296)
    model.addConstr(6*x3 <= 296)
    model.addConstr(8*x4 <= 296)
    model.addConstr(8*x5 <= 296)
    model.addConstr(11*x6 <= 296)
    model.addConstr(6*x7 <= 296)

    model.addConstr(5*x0 <= 214)
    model.addConstr(2*x1 <= 214)
    model.addConstr(6*x2 <= 214)
    model.addConstr(3*x3 <= 214)
    model.addConstr(5*x4 <= 214)
    model.addConstr(2*x5 <= 214)
    model.addConstr(9*x6 <= 214)
    model.addConstr(11*x7 <= 214)

    model.addConstr(13*x0 + x2 >= 16)
    model.addConstr(7*x1 + 8*x5 >= 19)
    model.addConstr(8*x4 + 11*x6 >= 18)
    model.addConstr(13*x0 + 8*x4 >= 17)
    model.addConstr(7*x1 + 6*x3 >= 19)
    model.addConstr(6*x3 + 8*x4 >= 21)
    model.addConstr(6*x3 + 8*x5 >= 18)
    model.addConstr(8*x5 + 6*x7 >= 13)

    model.addConstr(7*x1 + 6*x3 + 8*x4 >= 24)
    model.addConstr(13*x0 + x2 + 8*x5 >= 24)
    model.addConstr(13*x0 + 7*x1 + 11*x6 >= 24)
    model.addConstr(7*x1 + 8*x5 + 6*x7 >= 24)
    model.addConstr(6*x3 + 8*x4 + 6*x7 >= 24)
    model.addConstr(8*x4 + 11*x6 + 6*x7 >= 24)
    model.addConstr(x2 + 8*x5 + 11*x6 >= 24)
    model.addConstr(7*x1 + x2 + 6*x3 >= 24)
    model.addConstr(7*x1 + x2 + 6*x7 >= 24)
    model.addConstr(13*x0 + x2 + 6*x7 >= 24)
    model.addConstr(6*x3 + 8*x5 + 8*x7 >= 24)
    model.addConstr(x2 + 6*x3 + 8*x5 >= 24)
    model.addConstr(13*x0 + 8*x5 + 6*x7 >= 24)
    model.addConstr(13*x0 + 6*x3 + 8*x4 >= 24)
    model.addConstr(13*x0 + 7*x1 + 8*x4 >= 24)
    model.addConstr(7*x1 + 8*x4 + 6*x7 >= 24)

    model.addConstr(x0 >= 0)
    model.addConstr(x1 >= 0)
    model.addConstr(x2 >= 0)
    model.addConstr(x3 >= 0)
    model.addConstr(x4 >= 0)
    model.addConstr(x5 >= 0)
    model.addConstr(x6 >= 0)
    model.addConstr(x7 >= 0)

    model.addConstr(x0 % 1 == 0)
    model.addConstr(x1 % 1 == 0)
    model.addConstr(x2 % 1 == 0)
    model.addConstr(x3 % 1 == 0)
    model.addConstr(x4 % 1 == 0)
    model.addConstr(x5 % 1 == 0)
    model.addConstr(x6 % 1 == 0)
    model.addConstr(x7 % 1 == 0)

    model.optimize()

    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Objective: ", model.objval)
        print("Postage stamps: ", x0.varValue)
        print("Manila envelopes: ", x1.varValue)
        print("3D printers: ", x2.varValue)
        print("Packs of paper: ", x3.varValue)
        print("Lanyards: ", x4.varValue)
        print("Paper clips: ", x5.varValue)
        print("Red pens: ", x6.varValue)
        print("Color printers: ", x7.varValue)
    else:
        print("No solution found")

solve_optimization_problem()
```