## Step 1: Define the optimization problem
The problem is to maximize the given objective function subject to various constraints. The objective function and constraints are defined based on the provided attributes and resources for 'bowls of instant ramen', 'steaks', 'peanutbutter sandwiches', and 'granola bars'.

## Step 2: Identify the variables
Let $x_0$ be the number of bowls of instant ramen, $x_1$ be the number of steaks, $x_2$ be the number of peanutbutter sandwiches, and $x_3$ be the number of granola bars.

## 3: Formulate the objective function
The objective function to maximize is:
\[ 3.62x_0^2 + 4.63x_0x_1 + 5.03x_0x_3 + 2.07x_1^2 + 6.03x_1x_2 + 3.6x_1x_3 + 6.97x_2^2 + 7.45x_2x_3 + 4.02x_3^2 + 9.15x_0 + 9.81x_1 + 8.4x_3 \]

## 4: Define the constraints
### Resource Constraints
- Protein constraints:
  - $3.51x_0 + 0.65x_1 + 8.37x_2 + 1.67x_3 \leq 139$
  - $8.37^2x_2^2 + 1.67^2x_3^2 \leq 44$
  - $3.51x_0 + 0.65x_1 \leq 59$
  - $3.51x_0 + 8.37x_2 \leq 104$
  - $0.65^2x_1^2 + 1.67^2x_3^2 \leq 95$
  - $3.51x_0 + 0.65x_1 + 8.37x_2 \leq 65$
  - $3.51x_0 + 0.65x_1 + 8.37x_2 + 1.67x_3 \leq 65$

- Carbohydrates constraints:
  - $5.28^2x_1^2 + 7.08^2x_2^2 \leq 59$
  - $1.79x_0 + 7.08x_2 \leq 56$
  - $1.79x_0 + 5.28x_1 \leq 109$
  - $5.28^2x_1^2 + 7.75^2x_3^2 \leq 85$
  - $1.79x_0 + 5.28x_1 + 7.08x_2 + 7.75x_3 \leq 85$

- Tastiness rating constraints:
  - $7.74x_0 + 6.01x_2 \geq 29$
  - $7.74x_0 + 6.01x_2 \leq 140$
  - $7.74^2x_0^2 + 7.62^2x_3^2 \leq 56$
  - $7.25x_1 + 6.01x_2 \leq 105$
  - $7.74x_0 + 7.25x_1 + 6.01x_2 + 7.62x_3 \leq 105$

### Variable Constraints
- $x_0, x_1, x_2, x_3$ are integers.

## 5: Implement the optimization problem using Gurobi
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="bowls_of_instant_ramen", vtype=gp.GRB.INTEGER)
x1 = m.addVar(name="steaks", vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="peanutbutter_sandwiches", vtype=gp.GRB.INTEGER)
x3 = m.addVar(name="granola_bars", vtype=gp.GRB.INTEGER)

# Objective function
m.setObjective(3.62*x0**2 + 4.63*x0*x1 + 5.03*x0*x3 + 2.07*x1**2 + 6.03*x1*x2 + 3.6*x1*x3 + 
               6.97*x2**2 + 7.45*x2*x3 + 4.02*x3**2 + 9.15*x0 + 9.81*x1 + 8.4*x3, gp.GRB.MAXIMIZE)

# Constraints
# Protein constraints
m.addConstr(3.51*x0 + 0.65*x1 + 8.37*x2 + 1.67*x3 <= 139)
m.addConstr(8.37**2*x2**2 + 1.67**2*x3**2 <= 44)
m.addConstr(3.51*x0 + 0.65*x1 <= 59)
m.addConstr(3.51*x0 + 8.37*x2 <= 104)
m.addConstr(0.65**2*x1**2 + 1.67**2*x3**2 <= 95)
m.addConstr(3.51*x0 + 0.65*x1 + 8.37*x2 <= 65)
m.addConstr(3.51*x0 + 0.65*x1 + 8.37*x2 + 1.67*x3 <= 65)

# Carbohydrates constraints
m.addConstr(5.28**2*x1**2 + 7.08**2*x2**2 <= 59)
m.addConstr(1.79*x0 + 7.08*x2 <= 56)
m.addConstr(1.79*x0 + 5.28*x1 <= 109)
m.addConstr(5.28**2*x1**2 + 7.75**2*x3**2 <= 85)
m.addConstr(1.79*x0 + 5.28*x1 + 7.08*x2 + 7.75*x3 <= 85)

# Tastiness rating constraints
m.addConstr(7.74*x0 + 6.01*x2 >= 29)
m.addConstr(7.74*x0 + 6.01*x2 <= 140)
m.addConstr(7.74**2*x0**2 + 7.62**2*x3**2 <= 56)
m.addConstr(7.25*x1 + 6.01*x2 <= 105)
m.addConstr(7.74*x0 + 7.25*x1 + 6.01*x2 + 7.62*x3 <= 105)

# Optimize
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("bowls_of_instant_ramen: ", x0.varValue)
    print("steaks: ", x1.varValue)
    print("peanutbutter_sandwiches: ", x2.varValue)
    print("granola_bars: ", x3.varValue)
else:
    print("The model is infeasible")
```