algebra precalculus - How to find the least number of objects in a problem involving profits?

The problem is as follows:

In an electronics factory, the owner calculates that the cost to
produce his new model of portable TV is $26$ dollars. After meeting
with the distributors, he agrees the sale price for his new product to
be $25$ dollars each and additionally $8\%$ more for each TV set sold
after $8000$ units. What is the least number of TV's he has to sell in
order to make a profit?.

The answers are:

• 16000


• 15001


• 16001


• 15999


• 17121

This problem has made me to go in circles on how to express it in a mathematical expression. I'm not sure if it does need to use of inequations.

What I tried to far is to think this way:

The first scenario is what if what he sells is $8000$ units, then this would become into:

$$\textrm{production cost:}\,26\frac{\$}{\textrm{unit}} \times 8000\,\textrm{units} = 208000\,\$$$

$$\textrm{sales:}\,25\frac{\$}{\textrm{unit}} \times 8000\,\textrm{units}=\,200000\,\$$$

Therefore there will be an offset of $8000\,\$$ as

$$208000\$-200000\$\,=\,8000\,\$$$

So I thought what If I consider the second part of the problem which it says that he will receive an additional of $8\%$ after $8000$ units.

Therefore his new sale price will be $27\,\$$ because:

$$25+\frac{8}{100}\left(25\right )=27\,\$$$

So from this I thought that this can be used in the previous two relations.
But how?.

I tried to establish this inequation:

$$26\left(8000+x\right)<25\left(8000\right)+27\left(8000+x\right)$$

But that's where I'm stuck at since it is not possible to obtain a reasonable result from this as one side will be negative and the other positive.

The logic I used was to add up $8000\,\$$ plus something which is the production cost must be less than what has been obtained from selling the first $8000$ units plus a quantity to be added to those $8000$.

However there seems to be an error in this approach. Can somebody help me to find the right way to solve this problem?