II) 80 units
Solving the II question:
1) Considering that the maximum profit is obtained by
P(x) = R(x) - C(x) Plugging into that those functions:
P(x) = 20x -0.1x²-(4x+2)
P(x) = 20x - 0.1x² -4x -2 Rewriting it
P(x)= -0.1x² +16x -2
2) The number of units that must be sold is the x-coordinate of the Vertex of that parabola since the Y-axis is the Profit P(x) and this is found by the following formula:
[tex]X_V=-\frac{b}{2a}=\frac{-16}{2(-0.1)}=\frac{-16}{-0.2}=80[/tex]
By the way, the Maximum profit (Question I), (Maximum point), on the other hand, is the Y-vertex:
[tex]Y_V=\frac{-\Delta}{4a}=\frac{-(16^2-4(-0.1)(-2)_{}}{4(-0.1)}=638[/tex]
As we can see here:
3) Hence, the answer is 80 units that yield a maximum profit of $638
