Answer to Question #314077 in Algebra for Ravele

Question

The demand function of a firm is

Q=90−1,5P,

where P and Q represent the price and quantity, respectively. At what price is revenue a maximum?

Answer 1

The given demand function is

$Q=90-1.5P$

Revenue (R)=Q.P

$R=(90-1.5P).P$

For the maximum review,

$\frac{dR}{dP}=0$

$\Rightarrow 90-3P=0$

$\Rightarrow P= 30$

Hence, price should be equal to 30.