Here's the Gurobi code that captures the described optimization problem:

```python
from gurobipy import Model, GRB

# Create a new model
m = Model("optimization_problem")

# Create variables
tomatoes = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="tomatoes")
corn_cobs = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="corn_cobs")

# Set objective function
m.setObjective(3.97 * tomatoes + 3.18 * corn_cobs, GRB.MINIMIZE)

# Add constraints
m.addConstr(0.53 * tomatoes + 2.22 * corn_cobs >= 7, "healthiness_min")
m.addConstr(4.2 * tomatoes + 2.22 * corn_cobs >= 19, "fat_min")
m.addConstr(0.28 * tomatoes + 4.12 * corn_cobs >= 5, "umami_min")
m.addConstr(-7 * tomatoes + 1 * corn_cobs >= 0, "custom_constraint")

m.addConstr(0.53 * tomatoes + 2.22 * corn_cobs <= 14, "healthiness_max")
m.addConstr(4.2 * tomatoes + 2.22 * corn_cobs <= 47, "fat_max")
m.addConstr(0.28 * tomatoes + 4.12 * corn_cobs <= 7, "umami_max")


# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    print('tomatoes:', tomatoes.x)
    print('corn_cobs:', corn_cobs.x)
elif m.status == GRB.INFEASIBLE:
    print('The model is infeasible.')
else:
    print('Optimization ended with status %d' % m.status)

```
