The price-demand function is . That is, is the price in dollars at which knobs can be sold.
How many knobs can be sold at a price of $ 33.9?
Write an equation for the revenue function R(x).
Price of a knob is $33.9
Let x be the number of knobs sold.
Revenue is the income after selling the knob and with every knob sold the revenue increases by $33.9 so 33.9 is the rate of the change of ravenue and may be taken as slope of the function.
Now as the rate of change is constant, therefore we can say that the revenue function is a straight line. Let this function be f(x).
We also know that if no knob is sold than the revenue is equal to zero. Hence for x = 0, f(x) = 0.
We know that the function of a straight line is:
f(x) = mx +c
where m is the slope and c is the intercept or value of the function for x = 0
therefore the revenue function is: f(x) = 33.9x