The revenue function in terms of the number of units sold ,x, is given as
R=370 x - 0.3 x^2
where R is the total revenue in dollars. Find the number of units sold x that produces a maximum revenue?

Please explain?

Question

The revenue function in terms of the number of units sold ,x, is given as
R=370 x - 0.3 x^2
where R is the total revenue in dollars. Find the number of units sold x that produces a maximum revenue?

Please explain?

anonymous · Answer

1) draw a picture for 
$$R = -0.3x^2 +370x=-0.3x\left(x-\frac{3700}{3}\right)$$
You probably need the vertex equation 
|dw:1351724488503:dw|

anonymous · Answer

Explanation: 
If you can factor the expression so that it is only made up of products
y= (x-?)(x-?) then you know that when each parenthesis is equal to zero you have y=0. 
So when x=0, (-.3x)=0 and therefore r(x)=0
When x=3700/3 then (3700/3 -3700/3) = 0 and therefore y=0

Parabolas are symmetric, so since x=0 and x=3700/3 have the same y, you can argue that the x value between them (3700/3)/2 should be where the vertex is. Then plug x=(3700/3)/2 into R(x) = -0.3x(x-(3700/2)) for R