To solve this optimization problem, we first need to define the variables, objective function, and constraints using Gurobi's Python interface.

```python
import gurobi as gp

# Define the variables
m = gp.Model("optimization_problem")

hot_dogs = m.addVar(name="hot_dogs", vtype=gp.GRB.INTEGER)
lemons = m.addVar(name="lemons", vtype=gp.GRB.INTEGER)
apple_pies = m.addVar(name="apple_pies", vtype=gp.GRB.INTEGER)
apples = m.addVar(name="apples", vtype=gp.GRB.INTEGER)
fruit_salads = m.addVar(name="fruit_salads", vtype=gp.GRB.INTEGER)
corn_cobs = m.addVar(name="corn_cobs", vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(8 * hot_dogs + 7 * lemons + 8 * apple_pies + apples + 7 * fruit_salads + 9 * corn_cobs, gp.GRB.MAXIMIZE)

# Define the resources/attributes
resources = {
    'r0': {'description': 'umami index', 'upper_bound': 501, 'x0': 2.61, 'x1': 5.18, 'x2': 17.84, 'x3': 5.81, 'x4': 11.17, 'x5': 15.47},
    'r1': {'description': 'milligrams of calcium', 'upper_bound': 259, 'x0': 18.21, 'x1': 7.26, 'x2': 1.81, 'x3': 9.8, 'x4': 1.04, 'x5': 6.24},
    'r2': {'description': 'healthiness rating', 'upper_bound': 602, 'x0': 9.96, 'x1': 0.42, 'x2': 0.39, 'x3': 9.33, 'x4': 9.06, 'x5': 12.48}
}

# Add constraints for umami index
m.addConstr(5.18 * lemons + 17.84 * apple_pies + 5.81 * apples >= 59, name="umami_1")
m.addConstr(5.18 * lemons + 5.81 * apples + 15.47 * corn_cobs >= 59, name="umami_2")
m.addConstr(2.61 * hot_dogs + 11.17 * fruit_salads + 15.47 * corn_cobs >= 59, name="umami_3")
m.addConstr(5.18 * lemons + 17.84 * apple_pies + 11.17 * fruit_salads >= 59, name="umami_4")
m.addConstr(2.61 * hot_dogs + 5.18 * lemons + 11.17 * fruit_salads >= 59, name="umami_5")
m.addConstr(2.61 * hot_dogs + 17.84 * apple_pies + 15.47 * corn_cobs >= 59, name="umami_6")
m.addConstr(2.61 * hot_dogs + 5.18 * lemons + 15.47 * corn_cobs >= 59, name="umami_7")
m.addConstr(2.61 * hot_dogs + 5.18 * lemons + 5.81 * apples >= 59, name="umami_8")
m.addConstr(2.61 * hot_dogs + 17.84 * apple_pies + 5.81 * apples >= 59, name="umami_9")
m.addConstr(5.18 * lemons + 5.81 * apples + 11.17 * fruit_salads >= 59, name="umami_10")

# Add more constraints for umami index
m.addConstr(5.18 * lemons + 17.84 * apple_pies + 5.81 * apples >= 61, name="umami_11")
m.addConstr(5.18 * lemons + 5.81 * apples + 15.47 * corn_cobs >= 61, name="umami_12")
m.addConstr(2.61 * hot_dogs + 11.17 * fruit_salads + 15.47 * corn_cobs >= 61, name="umami_13")
m.addConstr(5.18 * lemons + 17.84 * apple_pies + 11.17 * fruit_salads >= 61, name="umami_14")
m.addConstr(2.61 * hot_dogs + 5.18 * lemons + 11.17 * fruit_salads >= 61, name="umami_15")
m.addConstr(2.61 * hot_dogs + 17.84 * apple_pies + 15.47 * corn_cobs >= 61, name="umami_16")
m.addConstr(2.61 * hot_dogs + 5.18 * lemons + 15.47 * corn_cobs >= 61, name="umami_17")
m.addConstr(2.61 * hot_dogs + 5.18 * lemons + 5.81 * apples >= 61, name="umami_18")
m.addConstr(2.61 * hot_dogs + 17.84 * apple_pies + 5.81 * apples >= 61, name="umami_19")
m.addConstr(5.18 * lemons + 5.81 * apples + 11.17 * fruit_salads >= 61, name="umami_20")

# Add constraints for calcium
m.addConstr(18.21 * hot_dogs + 1.04 * fruit_salads >= 16, name="calcium_1")
m.addConstr(1.04 * fruit_salads + 6.24 * corn_cobs >= 40, name="calcium_2")
m.addConstr(18.21 * hot_dogs + 7.26 * lemons >= 34, name="calcium_3")
m.addConstr(1.81 * apple_pies + 9.8 * apples + 1.04 * fruit_salads >= 43, name="calcium_4")
m.addConstr(18.21 * hot_dogs + 7.26 * lemons + 6.24 * corn_cobs >= 43, name="calcium_5")
m.addConstr(18.21 * hot_dogs + 7.26 * lemons + 9.8 * apples >= 43, name="calcium_6")
m.addConstr(7.26 * lemons + 9.8 * apples + 1.04 * fruit_salads >= 43, name="calcium_7")

# Add constraints for healthiness rating
m.addConstr(9.96 * hot_dogs + 9.33 * apples + 9.06 * fruit_salads >= 85, name="healthiness_1")
m.addConstr(9.96 * hot_dogs + 0.42 * lemons + 12.48 * corn_cobs >= 85, name="healthiness_2")
m.addConstr(0.39 * apple_pies + 9.06 * fruit_salads + 12.48 * corn_cobs >= 85, name="healthiness_3")

# Add constraints for other requirements
m.addConstr(8 * apples - 9 * corn_cobs >= 0, name="other_1")
m.addConstr(5.81 * apples + 11.17 * fruit_salads <= 284, name="other_2")
m.addConstr(5.18 * lemons + 11.17 * fruit_salads <= 252, name="other_3")
m.addConstr(2.61 * hot_dogs + 15.47 * corn_cobs <= 261, name="other_4")
m.addConstr(5.18 * lemons + 5.81 * apples <= 212, name="other_5")
m.addConstr(2.61 * hot_dogs + 17.84 * apple_pies <= 167, name="other_6")
m.addConstr(17.84 * apple_pies + 11.17 * fruit_salads <= 303, name="other_7")
m.addConstr(5.81 * apples + 15.47 * corn_cobs <= 210, name="other_8")
m.addConstr(5.18 * lemons + 15.47 * corn_cobs <= 297, name="other_9")
m.addConstr(2.61 * hot_dogs + 5.18 * lemons + 17.84 * apple_pies + 5.81 * apples + 11.17 * fruit_salads + 15.47 * corn_cobs <= 297, name="other_10")

# Solve the model
m.optimize()

# Print the results
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hot dogs: ", hot_dogs.varValue)
    print("Lemons: ", lemons.varValue)
    print("Apple pies: ", apple_pies.varValue)
    print("Apples: ", apples.varValue)
    print("Fruit salads: ", fruit_salads.varValue)
    print("Corn cobs: ", corn_cobs.varValue)
else:
    print("No optimal solution found")
```