The demand for widgets is given by q 80 l3p where q is the

The demand for widgets is given by q = 80 - (l/3)p, where q is the of widgets and p is the price in dollars. Find the revenue function R(x). Find the price that maximizes revenue. Find the maximum revenue. How many widgets must be produced to maximize revenue?

Solution

q=80- p/3

Revenue= price * number of widgets= (80 - p/3)p= 80p   - p²/3

b. To find the price that maximizes revenue,we have to find the vertex

Vertex, p=-b/2a= -80/2/3= 120

c. maximum revenue is at p=120

R(120)=80*120 - 120²/3= 9600- 4800=4800

d. q=80-p/3

p= 3(80-q)

R(q)= 3(80-q) * q= 240q - 3q²

q= -240/-6=40