Question 1175979
<font color=black size=3>
P(x) = x(200-0.05x) 
P(x) = 200x-0.05x^2
P(x) = -0.05x^2 + 200x + 0 
y = -0.05x^2 + 200x + 0 


The last equation is in the form y = ax^2+bx+c
where,
a = -0.05
b = 200
c = 0


The parabola opens downward because the leading coefficient a = -0.05 is negative. 
This means the vertex is the highest point where the max profit occurs. 
The vertex is (h,k) such that
h = -b/(2a)
h = -200/(2(-0.05))
h = 2000
and
k = P(h)
k = -0.05h^2 + 200h + 0
k = -0.05(2000)^2 + 200(2000) + 0
k = 200,000


If you sell x = 2000 units per day, then you'll reach the max profit of P = 200,000 dollars per day.
</font>