A company produces and sells two different products. Product A sells f

Your solution was correct until this point, but as soon as you start counting equations and unknowns, you are no longer answering the question that was asked. The question does not ask if you can solve for a or b individually -- only then would counting equations and unknowns even potentially be helpful (but with 3 unknowns, the rules are much more complicated than with only 2 unknowns). Instead the question asks merely whether the company made a profit. And if that's the question, the numbers genuinely matter. For example, if we knew the company's revenue was only $9 (one product of each type), the company clearly could not have covered their $500,000 fixed cost. Then we'd be sure they took a loss. If instead the company's revenue was $40 trillion, then since they profit on each sale, then no matter how the sales broke down between products A and B, the company would easily cover their $500,000 fixed cost, and we could be certain they made a profit.

We know the company profits $2 for each unit of product A sold, and $1 for each unit of product B. Their revenue is 5a + 4b. Using both Statements, we can consider two extreme scenarios. Their revenue from A was greater than their revenue from B. It's possible all of their revenue was from A. In that case, 5a = 1,500,000, and a = 300,000. We then know they make a profit of 2a = $600,000, which would indeed cover their $500,000 fixed cost. But it's also possible that their revenue from A is almost equal to their revenue from B. So it might be that their revenue from A is slightly greater than half of 1,500,000. Say it's exactly half, so 5a = 750,000. Then a = 150,000. We'd also have 4b = 750,000, and b = 187,500. Since their profit is 2a + b dollars, the profit is $487,500 (so would be negligibly greater than that if revenue from A is strictly greater than that from B). So it's possible, but only just, that the company fails to cover their $500,000 fixed cost, and the answer is E. But if the numbers were changed just slightly -- if the revenue were slightly higher, say, or the fraction of the revenue from A was slightly higher -- the answer would be C, or possibly A, depending on the details.

Possibly the best advice I can give to a GMAT test taker who is counting equations and unknowns to solve DS questions is to stop counting equations and unknowns. I've broken down large pools of official DS questions by difficulty level, and have then evaluated how often one would get a right answer by unthinkingly counting equations and unknowns. Even at the medium level, you only get a right answer 1/3 of the time (and the same is true at the hard level), which is almost like guessing randomly when you consider that in DS one or two answer choices can often be ruled out instantly. If you're reading prep company material that recommends the strategy, I'd advise finding better material to study from.

the company sold the same number of units of each product as it produced. => a and b are equal ....
Could you please verify this?

To come up 1.5M revenue within “ the company sold the same number of units of each product as it produced.” statement a=b It should produce 166666.7777 products each. This makes No profit or no loss and give Yes to A.

Which point did I miss?

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That's not what that sentence means. If the sentence said:

"The company sold the same number of units of each product."

without the extra words at the end, then that would mean a = b. But as written, the sentence is not comparing how many units of A were sold and how many of B were sold. It is comparing how many units of A were sold and how many units of A were produced, and similarly for B. It's just saying that the company sold every unit that it made.

As I pointed out in my post above, the wording here is not exactly like what you'd see on the GMAT. There are simpler ways to express what this sentence is attempting to express, and I'd expect a real GMAT question to use simpler language than this one does.

The answer is D. Correct me if I am wrong.

There appears to be an error near the top of your solution, in the line beginning "1)...". You rewrite the equation 1,500,000 = 5a + 4b as k = 1,500,000 - 3b, but if you just replace k with 2a + b, which is how you've defined k, you'll see those two equations aren't the same; the second equation would need to say k = 1,500,000 - 3b - 3a, or you'd need different coefficients. You also didn't analyze Statement 2 alone, and that Statement is clearly insufficient (because the company could sell merely one product of each type, in which case they certainly lose money).

I explained this above using an algebraic approach, because I was replying to someone using an algebraic solution, but this problem is really just a weighted average question. The company earns revenue from two sources. Ignoring the $500,000 fixed cost for now, on one source, they make a 25% profit (costs are 75% of revenue) and on the other they make a 40% profit (costs are 60% of revenue). So when we combine the two revenue streams, the profit will be somewhere between 25% and 40%. When we learn the company earns more revenue from the more profitable source, we learn that their percent profit is above the midpoint of 25% and 40%, so is above 32.5%. We know also their total revenue is $1,500,000. So the company makes between 32.5% and 40% of $1,500,000 in profit, before we consider their fixed cost. We want to know if that profit exceeds the $500,000 fixed cost. And we can't tell, because 0.325*1,500,000 is just less than $500,000, while 0.4*1,500,000 is greater than $500,000. So the answer is E. You can prove that numerically if you want to; if you let the revenue from A be $800,000 and let the revenue from B be $700,000, and work out the total costs, you'll find they exceed the total revenue by a very small amount.