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

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

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

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

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

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

$$q_1\approx11, q_2\approx89$$