If the demand equation is p 2000 6q find the maximum reven

   If the demand equation is p = 2000 – 6q, find the maximum revenue. (Hint: Revenue is number of units sold times price.)

Solution

Demand p = 2000 - 6q

==> Revenue = pq

==> R(q) = (2000 - 6q)q = 2000q - 6q²

Maximum revenue ==> R \'(q) = 0

==> 2000(1) - 6(2)q^2-1 = 0

==> 2000 - 12q = 0

==> 12q = 2000

==> q = 2000/12

==> q = 166.67

Maximum revenue occurs when 167 units are sold

Maximum revenue = R(167) = 2000(167) - 6(167)²

==> R(167) = 166666

Hence maximum revenue = 166666