## Problem Description and Formulation

The problem is an optimization problem with the objective to minimize a linear function subject to several linear constraints. The variables are:

- $x_0$: milligrams of vitamin A
- $x_1$: milligrams of vitamin B5
- $x_2$: milligrams of vitamin B3
- $x_3$: milligrams of iron

The objective function to minimize is:

\[ 9.87x_0 + 2.03x_1 + 7.26x_2 + 4.87x_3 \]

Subject to the following constraints:

1. Muscle growth index for each vitamin/iron is given but directly translates to variable values: $x_0 = 29$, $x_1 = 21$, $x_2 = 31$, $x_3 = 29$.
2. $x_1 + x_3 \geq 26$
3. $x_0 + x_3 \geq 41$
4. $x_0 + x_1 \geq 27$
5. $x_1 + x_2 \geq 71$
6. $x_2 + x_3 \geq 31$
7. $x_0 + x_2 \geq 39$
8. $x_1 + x_2 + x_3 \geq 56$
9. $x_0 + x_1 + x_2 + x_3 \geq 56$
10. $7x_1 - 4x_3 \geq 0$
11. $x_1 + x_2 \leq 293$
12. $x_0 + x_2 \leq 184$
13. $x_0$ is an integer
14. $x_1$ is an integer
15. $x_2$ can be a non-integer
16. $x_3$ can be a non-integer

However, upon closer inspection, constraints 1 directly set the values of $x_0, x_1, x_2, x_3$ to specific numbers. This seems to contradict the nature of an optimization problem where these values are typically decision variables to be determined. 

Given the direct assignments:
- $x_0 = 29$
- $x_1 = 21$
- $x_2 = 31$
- $x_3 = 29$

Let's verify if these satisfy all constraints before proceeding with formulating the problem in Gurobi code.

## Verification of Given Values Against Constraints

1. $21 + 29 = 50 \geq 26$ - Satisfied
2. $29 + 29 = 58 \geq 41$ - Satisfied
3. $29 + 21 = 50 \geq 27$ - Satisfied
4. $21 + 31 = 52 \geq 71$ - Not satisfied
5. $31 + 29 = 60 \geq 31$ - Satisfied
6. $29 + 31 = 60 \geq 39$ - Satisfied
7. $21 + 31 + 29 = 81 \geq 56$ - Satisfied
8. $29 + 21 + 31 + 29 = 110 \geq 56$ - Satisfied
9. $7*21 - 4*29 = 147 - 116 = 31 \geq 0$ - Satisfied
10. $21 + 31 = 52 \leq 293$ - Satisfied
11. $29 + 31 = 60 \leq 184$ - Satisfied

Given that constraint 4 is not satisfied ($52 \geq 71$ is false), the problem as described with the given values for $x_0, x_1, x_2, x_3$ is infeasible.

## Gurobi Code Formulation

However, to adhere to your request and demonstrate how one might approach formulating this problem, here's how you could do it in Gurobi, keeping in mind the issue with constraint satisfaction:

```python
import gurobi as gp

# Create a new model
m = gp.Model("Vitamin_Optimization")

# Define variables
x0 = m.addVar(name="Vitamin_A", vtype=gp.GRB.INTEGER)  # milligrams of vitamin A
x1 = m.addVar(name="Vitamin_B5", vtype=gp.GRB.INTEGER)  # milligrams of vitamin B5
x2 = m.addVar(name="Vitamin_B3")  # milligrams of vitamin B3
x3 = m.addVar(name="Iron")  # milligrams of iron

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

# Constraints
m.addConstr(x1 + x3 >= 26)
m.addConstr(x0 + x3 >= 41)
m.addConstr(x0 + x1 >= 27)
m.addConstr(x1 + x2 >= 71)
m.addConstr(x2 + x3 >= 31)
m.addConstr(x0 + x2 >= 39)
m.addConstr(x1 + x2 + x3 >= 56)
m.addConstr(x0 + x1 + x2 + x3 >= 56)
m.addConstr(7*x1 - 4*x3 >= 0)
m.addConstr(x1 + x2 <= 293)
m.addConstr(x0 + x2 <= 184)

# Solve the problem
m.optimize()

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

Given the infeasibility based on the initial values provided and constraint 4 not being satisfied, running this code would reflect that the problem as initially laid out does not have a feasible solution based on the direct assignments given.