Question

The price P for demand D is given as P = 183 + 120D - 3D². Find d for which the price is increasing.

Answer 1

Price function P is given by
P = 183 + 120D - 3D²
Differentiating w.r. t. d.
`(dP)/(dD)` = 120 - 6D
If price is increasing, then we have
`(dP)/(dD)` > 0
∴ 120 - 6D > 0
∴ 6D < 120
∴ D < 20
∴ If demand is less than 20 units then price increases.