The problem is formulated as a linear program (LP) using Gurobi. The objective is to minimize the cost, which is a linear combination of the milligrams of calcium and vitamin B7. The constraints are linear inequalities representing the minimum and maximum resource requirements. The calcium amount is constrained to be an integer.

```python
from gurobipy import Model, GRB

# Create a new model
model = Model("nutrition_optimization")

# Create variables
calcium = model.addVar(vtype=GRB.INTEGER, name="calcium")
vitamin_b7 = model.addVar(name="vitamin_b7")

# Set objective function
model.setObjective(5.78 * calcium + 5.62 * vitamin_b7, GRB.MINIMIZE)

# Add constraints
model.addConstr(13 * calcium + 11 * vitamin_b7 >= 44, "kidney_support_min")
model.addConstr(13 * calcium + 11 * vitamin_b7 <= 98, "kidney_support_max")

model.addConstr(1 * calcium + 1 * vitamin_b7 >= 15, "cognitive_performance_min")
model.addConstr(1 * calcium + 1 * vitamin_b7 <= 53, "cognitive_performance_max")

model.addConstr(13 * calcium + 11 * vitamin_b7 >= 13, "muscle_growth_min")
model.addConstr(13 * calcium + 11 * vitamin_b7 <= 34, "muscle_growth_max")

model.addConstr(4 * calcium - 9 * vitamin_b7 >= 0, "additional_constraint")


# Optimize model
model.optimize()

# Print results
if model.status == GRB.OPTIMAL:
    print(f"Optimal solution found:")
    print(f"  Calcium: {calcium.x}")
    print(f"  Vitamin B7: {vitamin_b7.x}")
    print(f"  Objective value: {model.objVal}")
elif model.status == GRB.INFEASIBLE:
    print("Model is infeasible.")
else:
    print(f"Optimization terminated with status {model.status}")

```
