Question

he cost of running a small factory is modeled by the function

C(x) = x^3 - 3 x^2 + 17 x

i found that r(x) = 41x but how do i found the p profit =P(x)?

Answer 1

the cost of running a small factory is modeled by the function C(x) = x^3 - 3 x^2 + 17 x i found that r(x) = 41x but how do i find the profit =P(x)?

Answer 2

P(x)=R(x)-C(x)

Answer 3

r(x) is revenue, correct?

Answer 4

yes

Answer 5

so 41x-( x^3-3x^2+17x)?

Answer 6

right

Answer 7

i got -x^3+3x+24

Answer 8

p(x)=-x^3+3x+24

Answer 9

p(x)=41x-(x^3-3x^2+17x)
p(x)=-x^3+3x^2+24x

Answer 10

oh yeah the x

Answer 11

how do i maximize the profit? from that equation

Answer 12

take the derivative, find the max

Answer 13

deriv of the profit equation?

Answer 14

the 2nd deriv test to solve the max parabo;a

Answer 15

their asking me to Find the number of routers sold which will maximize weekly profit.

Answer 16

so what's the derivative of p(x)?

Answer 17

-3x^2+6x+24 or 3x^2+6x+23

Answer 18

the 1st one

Answer 19

ok the negative 1 confused me

Answer 20

so set it to 0

Answer 21

for the first derivative test, yes

Answer 22

im tryin to factor out -3(x+3)(x-8)=0

Answer 23

is it right so far?

Answer 24

i dont know how to find the vertex (the algebra way)

Answer 25

-3(x^2-2x-8)

Answer 26

-3(x-4)(x+2)

Answer 27

so x= 4 , -2

Answer 28

yes, can't sell negative number of routers, so -2 is garbage

Answer 29

2nd derivative is?

Answer 30

and plug that back into the original equation

Answer 31

no wait 2nd deriv

Answer 32

30?

Answer 33

hmm why the hell is this not working

Answer 34

hmm why the hell is this not working

Answer 35

p(x)=-x^3+3x^2+24x
p'(x)=-3x^2+6x+24
-3(x^2-2x-8)=0
x^2-2x-8=0
(x-4)(x+2)=0
x=4,-2
Oh, okay, i kept using 3x instead of 3x^2

Answer 36

p''(x)=-6x+6
p''(4)=-6(4)+6=-24+6=-18
f''(4)<0, maximum at x=4

Answer 37

plug 4 into original equation