## Problem Description and Symbolic Representation

The bodybuilder wants to minimize his costs while ensuring he gets a minimum of 80 grams of protein, 50 grams of fat, and 100 grams of carbs from Protein Bar A and Protein Bar B.

Let's define the symbolic variables:
- $x_1$ : Number of Protein Bar A
- $x_2$ : Number of Protein Bar B

The nutritional content of each bar and their costs are as follows:
- Protein Bar A: 10g protein, 3g fat, 11g carbs, $7
- Protein Bar B: 15g protein, 5g fat, 8g carbs, $10

## Objective Function and Constraints

The objective is to minimize the total cost: $7x_1 + 10x_2$

The constraints are:
1. Protein: $10x_1 + 15x_2 \geq 80$
2. Fat: $3x_1 + 5x_2 \geq 50$
3. Carbs: $11x_1 + 8x_2 \geq 100$
4. Non-negativity: $x_1 \geq 0, x_2 \geq 0$
5. Integer: $x_1, x_2$ are integers (though Gurobi can handle this, specifying it might not be necessary for the solver to find an integer solution if it exists)

## Symbolic Representation

```json
{
    'sym_variables': [('x1', 'Protein Bar A'), ('x2', 'Protein Bar B')],
    'objective_function': '7*x1 + 10*x2',
    'constraints': [
        '10*x1 + 15*x2 >= 80',
        '3*x1 + 5*x2 >= 50',
        '11*x1 + 8*x2 >= 100',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code

```python
import gurobipy as gp

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

# Define variables
x1 = m.addVar(name="Protein_Bar_A", lowBound=0, vtype=gp.GRB.INTEGER)  # Number of Protein Bar A
x2 = m.addVar(name="Protein_Bar_B", lowBound=0, vtype=gp.GRB.INTEGER)  # Number of Protein Bar B

# Objective function: minimize cost
m.setObjective(7 * x1 + 10 * x2, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(10 * x1 + 15 * x2 >= 80, name="protein_constraint")  # Protein constraint
m.addConstr(3 * x1 + 5 * x2 >= 50, name="fat_constraint")  # Fat constraint
m.addConstr(11 * x1 + 8 * x2 >= 100, name="carbs_constraint")  # Carbs constraint

# Solve the model
m.solve()

# Print the results
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
    print(f"Minimum cost: ${7 * x1.varValue + 10 * x2.varValue}")
else:
    print("No optimal solution found.")
```