Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

* `x`: Number of glasses of orange juice.
* `y`: Number of glasses of apple juice.

**Objective Function:**

Minimize `z = 7x + y` (Total Glycine intake)

**Constraints:**

* `2x + 5y >= 30` (Lysine requirement)
* `3x + 5y >= 40` (Alanine requirement)
* `5x + 2y <= 50` (Methionine limit)
* `x >= 0` (Non-negativity)
* `y >= 0` (Non-negativity)


```python
import gurobipy as gp
from gurobipy import GRB

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

# Create variables
x = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="orange_juice")
y = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="apple_juice")

# Set objective function
m.setObjective(7*x + y, GRB.MINIMIZE)

# Add constraints
m.addConstr(2*x + 5*y >= 30, "Lysine")
m.addConstr(3*x + 5*y >= 40, "Alanine")
m.addConstr(5*x + 2*y <= 50, "Methionine")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found:")
    print(f"  Orange Juice: {x.x}")
    print(f"  Apple Juice: {y.x}")
    print(f"  Minimum Glycine: {m.objVal}")
elif m.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status {m.status}")

```
