To solve this optimization problem using Gurobi, we will define the variables, objective function, and constraints according to the given specifications.

### Problem Formulation:

- **Variables:**
  - `x0`: milligrams of vitamin A (integer)
  - `x1`: milligrams of vitamin B5 (integer)
  - `x2`: milligrams of vitamin B3 (continuous)
  - `x3`: milligrams of iron (continuous)

- **Objective Function:** Minimize `9.87*x0 + 2.03*x1 + 7.26*x2 + 4.87*x3`

- **Constraints:**
  1. Muscle growth index for vitamin A: `29*x0`
  2. Muscle growth index for vitamin B5: `21*x1`
  3. Muscle growth index for vitamin B3: `31*x2`
  4. Muscle growth index for iron: `29*x3`
  5. Combined muscle growth index constraints:
     - `21*x1 + 29*x3 >= 26`
     - `29*x0 + 29*x3 >= 41`
     - `29*x0 + 21*x1 >= 27`
     - `21*x1 + 31*x2 >= 71`
     - `31*x2 + 29*x3 >= 31`
     - `29*x0 + 31*x2 >= 39`
     - `21*x1 + 31*x2 + 29*x3 >= 56`
     - `29*x0 + 21*x1 + 31*x2 + 29*x3 >= 56`
  6. Additional linear constraint: `7*x1 - 4*x3 >= 0`
  7. Upper bound constraints:
     - `21*x1 + 31*x2 <= 293`
     - `29*x0 + 31*x2 <= 184`

### Gurobi Code:

```python
from gurobipy import *

# Create a model
m = Model("Optimization_Problem")

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="vitamin_A")
x1 = m.addVar(vtype=GRB.INTEGER, name="vitamin_B5")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="vitamin_B3")
x3 = m.addVar(vtype=GRB.CONTINUOUS, name="iron")

# Objective function
m.setObjective(9.87*x0 + 2.03*x1 + 7.26*x2 + 4.87*x3, GRB.MINIMIZE)

# Constraints
m.addConstr(21*x1 + 29*x3 >= 26, "muscle_growth_index_1")
m.addConstr(29*x0 + 29*x3 >= 41, "muscle_growth_index_2")
m.addConstr(29*x0 + 21*x1 >= 27, "muscle_growth_index_3")
m.addConstr(21*x1 + 31*x2 >= 71, "muscle_growth_index_4")
m.addConstr(31*x2 + 29*x3 >= 31, "muscle_growth_index_5")
m.addConstr(29*x0 + 31*x2 >= 39, "muscle_growth_index_6")
m.addConstr(21*x1 + 31*x2 + 29*x3 >= 56, "muscle_growth_index_7")
m.addConstr(29*x0 + 21*x1 + 31*x2 + 29*x3 >= 56, "total_muscle_growth_index")
m.addConstr(7*x1 - 4*x3 >= 0, "linear_constraint")
m.addConstr(21*x1 + 31*x2 <= 293, "upper_bound_1")
m.addConstr(29*x0 + 31*x2 <= 184, "upper_bound_2")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Vitamin A: {x0.x}")
    print(f"Vitamin B5: {x1.x}")
    print(f"Vitamin B3: {x2.x}")
    print(f"Iron: {x3.x}")
else:
    print("No optimal solution found")
```