Producer/consumer, consumer thread never executed - c++

Question

Created a program having a producer thread and a consumer thread.
The producer thread continuously pushes to a stack every one second, which is protected by a mutex.
The consumer thread continuously pops from the stack.
The unexpected behavior is that, the producer thread is constantly running, while the consumer thread never gets a chance to pop the stack.
How could I proceed to investigate this problem? Many thanks.
#include <stack>
#include <chrono>
#include <thread>
#include <mutex>
#include <condition_variable>
#include <iostream>
std::mutex mtx;
std::stack<int> the_stack;
void producer(const int id)
{
while(1)
{
mtx.lock();
the_stack.push(0);
std::cout << "Producer " << id << " push" << std::endl;
std::this_thread::sleep_for(std::chrono::seconds(1));
mtx.unlock();
}
}//producer
void consumer(const int id)
{
while(1)
{
mtx.lock();
if (!the_stack.empty())
{
std::cout << "Consumer " << id << " pop" << std::endl;
the_stack.pop();
}
mtx.unlock();
}
}//consumer
int main()
{
std::thread thread_0(producer, 0);
std::thread consum_0(consumer, 0);
thread_0.join();
consum_0.join();
return 0;
}//main;

Answer 1

The producer is spending its sleeping time while holding the mutex.
This hardly gives the consumer a chance to lock the mutex.
If you put the sleep statement outside the mutex protected area, it will work as expected..
void producer(const int id)
{
while(1)
{
....
mtx.unlock();
std::this_thread::sleep_for(std::chrono::seconds(1)); // below the unlock operation
}