Here's the Gurobi code to solve the optimization problem. The code defines the variables, objective function, and constraints as described in the prompt.  It also includes the specified variable types (continuous or integer).

```python
import gurobipy as gp

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

    # Create variables
    vitamin_b1 = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="vitamin_b1")
    zinc = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="zinc")
    vitamin_b7 = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="vitamin_b7")
    carbohydrates = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="carbohydrates")
    potassium = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="potassium")
    vitamin_b4 = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="vitamin_b4")

    # Set objective function
    obj = (1 * vitamin_b1**2 + 8 * vitamin_b1 * zinc + 6 * vitamin_b1 * carbohydrates +
           2 * zinc**2 + 4 * zinc * vitamin_b7 + 3 * zinc * carbohydrates +
           3 * vitamin_b7**2 + 3 * vitamin_b7 * carbohydrates + 4 * carbohydrates**2 +
           7 * carbohydrates * potassium + 9 * potassium**2 + 3 * vitamin_b4**2 +
           4 * vitamin_b1 + 8 * vitamin_b7 + 2 * carbohydrates + 3 * potassium)
    m.setObjective(obj, gp.GRB.MINIMIZE)

    # Add constraints
    m.addConstr(5 * vitamin_b1 + 1 * zinc + 3 * vitamin_b7 + 5 * carbohydrates + 5 * potassium + 8 * vitamin_b4 <= 62, "r0")
    m.addConstr(3 * vitamin_b7 + 5 * carbohydrates >= 10, "c1")
    m.addConstr(1 * zinc + 5 * carbohydrates >= 5, "c2")
    m.addConstr(3 * vitamin_b7 + 5 * potassium >= 9, "c3")
    m.addConstr(3 * vitamin_b7 + 5 * carbohydrates <= 20, "c4")
    m.addConstr(1 * zinc + 3 * vitamin_b7 <= 17, "c5")
    m.addConstr(5 * carbohydrates + 8 * vitamin_b4 <= 57, "c6")
    m.addConstr(3 * vitamin_b7 + 8 * vitamin_b4 <= 59, "c7")
    m.addConstr(1 * zinc + 8 * vitamin_b4 <= 13, "c8")
    m.addConstr(5 * vitamin_b1 + 5 * potassium <= 57, "c9")
    m.addConstr(5 * vitamin_b1 + 1 * zinc + 5 * potassium <= 15, "c10")


    # Optimize model
    m.optimize()

    # Print solution
    if m.status == gp.GRB.OPTIMAL:
        print('Obj: %g' % m.objVal)
        for v in m.getVars():
            print('%s %g' % (v.varName, v.x))
    elif m.status == gp.GRB.INFEASIBLE:
        print('Optimization problem is infeasible.')
    else:
        print('Optimization ended with status %d' % m.status)


except gp.GurobiError as e:
    print('Error code ' + str(e.errno) + ': ' + str(e))

except AttributeError:
    print('Encountered an attribute error')
```