Answer
a. $30$
b. $4.8$
c. $-10$
Work Step by Step
We are given $q=5000 - 100p$
The cost function $C(q)=3000-20q+0.03q^2$
$P(q)=R(q)-C(q)$
$=(50q-\frac{1}{100}q^2)-(3000-20q+0.03q^2)$
$=70q-3000-0.04q^2$
The marginal profit from the sale of $q$ units is:
$P'(q)=70-0.08q$
a. $500$ units
When $q=500$, the marginal profit is
$P'(500)=70-0.08(500)=30$
b. $815$ units
When $q=815$, the marginal profit is
$P'(815)=70-0.08(815)=4.8$
c. b. $1000$ units
When $q=1000$, the marginal profit is
$P'(1000)=70-0.08(1000)=-10$
