Before taxation

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

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 in 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

(b)

q=\frac{55}{6}

(c)

q=10

(d)

q=\frac{25}{3}