To formulate Jamie's diet problem as a linear programming problem, we need to define the decision variables, objective function, and constraints.

Let's denote:
- $x_c$ as the number of units of chicken to eat.
- $x_b$ as the number of units of beef to eat.

The objective is to minimize the total cost of the diet. The cost per unit of chicken is $3.4, and the cost per unit of beef is $7.5. Thus, the objective function can be written as:
\[ \text{Minimize:} \quad 3.4x_c + 7.5x_b \]

The constraints are based on the nutritional requirements:
1. The diet must contain a minimum of 100 units of proteins.
2. The diet must contain a minimum of 60 units of fat.

Given that one unit of chicken has 10 units of proteins and 6 units of fat, and one unit of beef has 30 units of proteins and 40 units of fat, we can write the constraints as follows:
\[ 10x_c + 30x_b \geq 100 \] (protein constraint)
\[ 6x_c + 40x_b \geq 60 \] (fat constraint)

Also, since Jamie cannot eat a negative amount of food, we have non-negativity constraints:
\[ x_c \geq 0 \]
\[ x_b \geq 0 \]

Now, let's express this problem in Gurobi code using Python:

```python
from gurobipy import *

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

# Define the decision variables
x_c = m.addVar(name="chicken", vtype=GRB.CONTINUOUS, lb=0)
x_b = m.addVar(name="beef", vtype=GRB.CONTINUOUS, lb=0)

# Set the objective function
m.setObjective(3.4*x_c + 7.5*x_b, GRB.MINIMIZE)

# Add constraints
m.addConstr(10*x_c + 30*x_b >= 100, name="protein_constraint")
m.addConstr(6*x_c + 40*x_b >= 60, name="fat_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Chicken: {x_c.x}")
    print(f"Beef: {x_b.x}")
    print(f"Total cost: {m.objVal}")
else:
    print("No optimal solution found")
```