The demand equation for your company's virtual reality video headsets is

p=1,000

q^0.3

whereqis the total number of headsets that your company can sell in a week at a price ofpdollars. The total manufacturing and shipping cost amounts to$140per headset.

(a) Find the weekly cost, revenue and profit as a function of the demandqfor headsets.

C(q)=

R(q)=

P(q)=

(b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.)

q=headsets

What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.)

$

Second derivative test:

Your answer above is a critical point for the weekly profit function. To show it is a maximum, calculate the second derivative of the profit function.

P"(q)=

EvaluateP"(q) at your critical point. The result is

---Select---

negative

positive

, which means that the profit is

---Select---

concave up

concave down

at the critical point, and the critical point is a maximum.