Answer
a. 30
b. 0
c. -10
Work Step by Step
We are given $q=5000 - 100p \rightarrow p=\frac{5000-q}{100}$
$R(q)=qp=q(\frac{5000-q}{100})=\frac{5000q-q^2}{100}=50q-\frac{1}{100}q^2$
The marginal revenue is:
$R'(q)=50-\frac{1}{50}q$
a. $1000$ units
When $q=1000$, the marginal revenue is
$R'(1000)=50-\frac{1}{50}(1000)=30$
b. $2500$ units
When $q=2500$, the marginal revenue is
$R'(1000)=50-\frac{1}{50}(2500)=0$
c. b. $3000$ units
When $q=2500$, the marginal revenue is
$R'(1000)=50-\frac{1}{50}(3000)=-10$
