The dinggnat doorknob company intends to sell a new line of square doorknobs. the price-demand function is p ( x ) = 48.5 − 0.09 x p ( x ) = 48.5 - 0.09 x . that is, p ( x ) p ( x ) is the price in dollars at which x x knobs can be sold.

a. how many knobs can be sold at a price of $36.30?

b. write an equation for the revenue function r(x).

a. 135 doorknobs

b.

Step-by-step explanation:

The price-demand function is:

a. At a price of $36.30, the number of doorknobs sold, 'x' is:

Rounding it down to the nearest whole unit, the company can sell 135 doorknobs at $36.30

b. Revenue is the product of the price, p(x), by the demand, x. Therefore, the Revenue function is:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!