#Linear Programming


    # Create a linear programming problem

    # Create variables

    # Set objective function

    # Add constraints

    # Add additional constraint

    # Solve the problem

    # Check if a feasible solution exists

# Example usage
    # Example instance

    # Solve the "Linear Programming" problem

    # Print the result

if __name__ == '__main__':
    from pulp import LpProblem, LpVariable, LpMinimize, lpSum, value
    def linear_programming(V, D, C, B):
        prob = LpProblem("LinearProgramming", LpMinimize)
        X = [LpVariable(f"X{i}", lowBound=0) for i in range(len(V))]
        prob += lpSum(C[i] * X[i] for i in range(len(V)))
        for j in range(len(D)):
            prob += lpSum(V[j][i] * X[i] for i in range(len(V))) <= D[j]
        prob += lpSum(C[i] * X[i] for i in range(len(V))) - B >= 0
        prob.solve()
        if prob.status == 1:
            return True, [value(X[i]) for i in range(len(V))]
        else:
            return False, []
    if __name__ == '__main__':
        V = [[1, 2, 3], [4, 5, 6]]
        D = [10, 20]
        C = [1, 1, 1]
        B = 15
        feasible, solution = linear_programming(V, D, C, B)
        if feasible:
            print("A feasible solution exists:")
            print(solution)
        else:
            print("No feasible solution exists.")
