Can you explain why is it not worthwhile to produce under region three of production function?

First, let's review what the three regions of a production function are. That's about half of our answer right there.

We assume that we have one fixed factor of production---let's say capital---and one variable factor of production---let's say labor.

We can then graph the production function as the number of total goods produced as a function of the amount of labor we employ.

Region 1 is where marginal productivity of labor is increasing. Each new person-hour of work produces more than the last. As long as there is enough demand, we'd be silly not to continue producing more stuff---our production gets more efficient the more we make. This could happen because workers are complements for each other---we need a certain number of people to work each assembly line, and if we don't have enough we end up using a less efficient production process. Both capital and labor are used more efficiently as we add more labor.

Region 2 is where marginal productivity of labor is decreasing, but positive. Each new person-hour of work is less efficient than the last, but we do still produce more if we add more people or work them more hours. Most businesses in the real world operate in this regime---you may have already hired all the most qualified people, so adding new workers means reducing their average productivity, and if you work the people you have harder they get tired and don't do as much good work in the later hours. As we add more labor, the labor gets less efficient; but the capital gets more efficient because we're producing more overall output with the same fixed amount of capital.

Region 3 is where marginal productivity of labor is negative. Adding more person-hours actually makes our overall production worse. It's not simply that new workers aren't as good---that would be region 2. They are actively detracting from our productivity, perhaps by distracting other workers, or getting in their way, or producing substandard work that needs to be corrected. Or perhaps you're working your current workers so hard that they don't get enough sleep and start doing shoddy work all day long. Both capital and labor get less efficient as we add more labor.

Why is it rational to produce in regions 1 and 2 but not in region 3? Well, think about what we just said above: In region 3, as you add more person-hours your output gets worse. You are spending more money to make less product. It would never make sense to do that. You might do it by accident, thinking you are still in region 2; but you'd never do it on purpose if you're trying to maximize profits. A perfectly-rational business would never operate in region 3, but sometimes real-world businesses do because they don't realize it. In my opinion, any software company that works its programmers more than 40 hours per week (and many do) is in region 3---coding well requires thinking well, and thinking well requires resting well. (Of course, I could be wrong; maybe it's still region 2.)