manufacturer can produce digital recorders at a cost of $50 apiece. It is estimated that if the recorders are sold for p dollars apiece, consumers will buy q 120 p recorders each month.
Express the manufacturer’s profit P as a func- tion of q.
b. What is the average rate of profit obtained as the level of production increases from q 0 to q 20?
c. At what rate is profit changing when q 20 recorders are produced? Is the profit increasing or decreasing at this level of production?

Question

manufacturer can produce digital recorders at a cost of $50 apiece. It is estimated that if the recorders are sold for p dollars apiece, consumers will buy q   120   p recorders each month.
Express the manufacturer’s profit P as a func- tion of q.
b. What is the average rate of profit obtained as the level of production increases from q   0 to q   20?
c. At what rate is profit changing when q   20 recorders are produced? Is the profit increasing or decreasing at this level of production?

alones · Answer

Hrmm for each one?!? x.x
ANywyas for A:
$\  P = qp - $70q = q ~(p - $70) = q ~(120 - q - $70) = 50q - q^2$

$$\ B.$$ $\ DP/dq = 50 - 2q
$
$$\ C.$$
$\ dP/dq(20)$
Which would equal $\  = $10$