Here's the Gurobi code for the optimization problem.  The objective function is quadratic, and several constraints involve quadratic terms, making this a Quadratically Constrained Program (QCP).  Gurobi can handle these types of problems effectively. The code defines the variables, sets the objective function, and adds the constraints as specified in the problem description.

```python
import gurobipy as gp

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

# Create variables
b3 = m.addVar(lb=0, name="B3")  # milligrams of vitamin B3
e = m.addVar(lb=0, name="E")  # milligrams of vitamin E
b7 = m.addVar(lb=0, name="B7")  # milligrams of vitamin B7
b9 = m.addVar(lb=0, name="B9")  # milligrams of vitamin B9

# Set objective function
obj = 7 * b3**2 + 5 * b3 * e + 8 * b3 * b7 + 3 * e**2 + 2 * e * b7 + 8 * e * b9 + 7 * b7 * b9 + 4 * b9**2 + 6 * b3 + 3 * e + 2 * b9
m.setObjective(obj, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(8 * b3 + 5 * b9 >= 16, "c1")
m.addConstr(7 * e + 5 * b9 >= 11, "c2")
m.addConstr(7 * e + 3 * b7 + 5 * b9 >= 22, "c3")
m.addConstr(7 * e + 6 * b9 >= 7, "c4")
m.addConstr(3 * b3 + 8 * b7 >= 12, "c5")
m.addConstr(8 * b7 + 6 * b9 >= 10, "c6")
m.addConstr(3 * b3**2 + 7 * e**2 + 8 * b7**2 >= 10, "c7")
m.addConstr(3 * b3**2 + 7 * e**2 + 6 * b9**2 >= 10, "c8")
m.addConstr(3 * b3 + 7 * e + 8 * b7 >= 9, "c9")
m.addConstr(3 * b3 + 7 * e + 6 * b9 >= 9, "c10")
m.addConstr(6 * b3 + 3 * b9 >= 11, "c11")
m.addConstr(6 * e + 3 * b9 >= 10, "c12")
m.addConstr(6 * e + 6 * b7 >= 14, "c13")
m.addConstr(6 * b3 + 6 * e + 3 * b9 >= 21, "c14")
m.addConstr(-10 * b3**2 - 5 * b7**2 + 8 * b9**2 >= 0, "c15")
m.addConstr(8 * b3**2 + 7 * e**2 <= 110, "c16")
m.addConstr(7 * e + 3 * b7 <= 82, "c17")
m.addConstr(8 * b3**2 + 3 * b7**2 <= 65, "c18")
m.addConstr(8 * b3**2 + 7 * e**2 + 5 * b9**2 <= 64, "c19")
m.addConstr(8 * b3 + 7 * e + 3 * b7 + 5 * b9 <= 64, "c20")
m.addConstr(7 * e + 6 * b9 <= 41, "c21")
m.addConstr(3 * b3 + 7 * e <= 54, "c22")
m.addConstr(3 * b3 + 6 * b9 <= 70, "c23")
m.addConstr(3 * b3 + 7 * e + 8 * b7 + 6 * b9 <= 70, "c24")
m.addConstr(6 * b3 + 6 * b7 <= 66, "c25")
m.addConstr(6 * e**2 + 3 * b9**2 <= 35, "c26")
m.addConstr(6 * e + 6 * b7 <= 52, "c27")
m.addConstr(6 * b3 + 6 * e + 6 * b7 + 3 * b9 <= 52, "c28")
m.addConstr(3 * e + 1 * b7 <= 17, "c29")
m.addConstr(2 * b3**2 + 3 * b9**2 <= 17, "c30")
m.addConstr(2 * b3 + 1 * b7 <= 22, "c31")
m.addConstr(1 * b7 + 3 * b9 <= 26, "c32")
m.addConstr(3 * e + 1 * b7 + 3 * b9 <= 28, "c33")
m.addConstr(2 * b3 + 3 * e + 3 * b9 <= 21, "c34")
m.addConstr(2 * b3 + 1 * b7 + 3 * b9 <= 37, "c35")
m.addConstr(2 * b3 + 3 * e + 1 * b7 + 3 * b9 <= 37, "c36")


# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    for v in m.getVars():
        print('%s %g' % (v.varName, v.x))
else:
    print("Optimization failed. Status code:", m.status)

```
