Question

Given the total Revenue R(x) = 600x - 5x^2 and total cost C(x) = 100x + 10,500, Determine the quantity of x that maximized the profit.​

Answer 1

Answer:

hope this will help you

Step-by-step explanation:

Profit will be Pro(x)=xP−C(x)

Pro(x)=x(200−

400

x

)−(

100

x

2

+100x+40)

We want to maximize Pro(x) so differentiate it w.r.t x and put it =0

dx

d(Pro(x))

=200−

400

2x

−

100

2x

−100=0→x=4000

Hence, price per unit will be P=200−

400

4000

=190

Total Profit will be Pro(x)=4000×190−(

100

(4000)

2

+100×4000+40)=32×10

4

−40=319960.