Mathematics

Problem

Before taxation, a firm faces the demand equation

p = 70 - q

and has cost function

C(q)=2q^{2}+10q+100

, where

p

is the price per unit (dollars) and

q

is the quantity produced. A per-unit tax of \

5 is imposed, increasing the firm’s cost by

5 for every unit produced. After the tax, which of the following quantities maximizes profit? a)

q=11

q=\dfrac{55}{6}

q=10

q=\dfrac{25}{3}