Answer to Question #259676 in Algebra for Neng Santi Triamba

Question

If a firm's demand function is P = 100 - q, what quantities need to be sold to bring in a total revenue of £1000

Answer 1

$TR=pq=(100-q)q$

Substitute

$1000=100q-q^2, q\geq0$

$q^2-100q+1000=0$

$D=(-100)^2-4(1000)=6000$

$q=\dfrac{100\pm\sqrt{6000}}{2}$

$q=50\pm10\sqrt{15}$

$q_1\approx11, q_2\approx89$