A companys demand function is given by q 1346 30p What is

A company\'s demand function is given by q = 1346 – 30p. What is the company\'s marginal revenue at the point where they are selling 540 items ? Round your answer to the nearest cent. Hint: Remember that the Demand, Revenue, Cost, and Profit functions all use quantity (q) as the input. Therefore, in this problem, you first need to \"re-arrange\" the given function so that q is the input variable !

Solution

Demand Equation : q = 1346 – 30p

Write p in terms of q : 30p = 1346 -q

p = 1346/30 -q/30

Total Revnue function = p*q =(1346/30 -q/30)q

TR= 13460q/30 - q^2/30

marginal revenue is then calculated by taking the derivative of total revenue with respect to quantity

d(TR)/dQ = 13460/30 - q/15

q = 540 items Plug q in d(TR)/dQ = 13460/30 - q/15

marginal revenue d(TR)/dQ = 13460/30 -540/15 = 448.67 - 36 = 412.67