Answer:
a. 135 doorknobs
b. [tex]R(x) = 48.5x-0.09 x^2[/tex]
Step-by-step explanation:
The price-demand function is:
[tex]p(x) = 48.5-0.09 x[/tex]
a. At a price of $36.30, the number of doorknobs sold, 'x' is:
[tex]p(x) = 48.5-0.09 x\\36.30 = 48.5-0.09 x\\x= \frac{48.5-36.30}{0.09}\\x=135.55[/tex]
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:
[tex]R(x) = x*p(x)=x(48.5-0.09 x)\\R(x) = 48.5x-0.09 x^2[/tex]
