Question

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Answer 1

The profit function is P = R - C (the revenue is what you make, the cost is what you lose; the profit is the balance between them, essentially). If you substitute R and C into this and then find the point where its derivative is 0, it should yield the x-value for maximum profit selling x items. The second derivative test can confirm this because the second derivative at that x-value will tell you if the function is concave up or concave down (a maximum occurs when the graph is concave down).

Answer 2

So...
P = R - C
P = (2000x-x^2) - (800+1900x)
= 2000x - x^2 - 800 - 1900x
= 100x - x^2 - 800
= -x^2 + 100x - 800 (We can see here that the x^2 is negative, so the graph opens downward / has a maximum vertex, just noting!)

From there, we can take derivative of P and set it equal to 0.