Question 798620
a) {{{P(x) = -0.4x^2 + 80x - 1600 }}}


b) x=50
{{{P= -0.4*2500 + 4000 - 1600 = 1400}}}


c) 
Graph function takes 3 pairs of numbers before the equation.
First pair define the size of the image on the screen (width then height).
Set this to see the graph on the screen.
Second pair are the range of values on the x axis (min then max)
Third pair are the range of values on the y axis (min then max)
You can calculate some vaues, but I just set these wide to see the function. Using  (-1000, 1000) for both:
{{{graph(300,200,-1000,1000,-1000,1000,80x-0.4x^2-1600)}}}
Inspecting the result shows that the region of interest, (in this case the values where the maximum value of y occurs) lies at higher values of y (try -500,5000). The x values can be narrowed down (try -100,400).
{{{graph(300,200,-100,400,-500,5000,80x-0.4x^2-1600)}}}
Further adjustment (to -50,200,-300,2700) produces
{{{graph(300,200,-50,200,-300,2700,80x-0.4x^2-1600)}}}
Inspecting this shows the max lies around 100 sales
d) 
Max Profit @ x=100 sales
P=-4000+8000-1600=$2400
That sale brought in $80 and cost 199/2.5 =$79.60
Next sale brings in $80 but costs 201/2.5=$80.40