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).

Answer:a. 135 doorknobsb. [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 $36.30b. 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]