Question

Automobile Production, The number N of cars produced at a certain factory in 1 day after t hours of operation is given by N(t) = 100t – 5t2, 0 ≤ t ≤ 10. If the cost C (in dollars) of producing N cars is C(N) = 15,000 + 8000N, find the cost C as a function of the time t of operation of the factory.

Answer 1

what will u get if you replaced the N in the C(N) formula with 100t – 5t2 ?

Answer 2

@gwenisa r u there?

Answer 3

C(t) = 15000 + 8000( put here what u have for N(t) ) then expand the answer, can u do that?

Answer 4

sorry yes i an here

Answer 5

can you continue from here? you have the answer above , 90% of it, just got to do the remaining 10%, can you?

Answer 6

it's puzzling

Answer 7

I just need to know how to set the equation down

Answer 8

C(t) = 15000 + 8000 (100t - 5t2)
C(t) = 15000 + 800000t - 40000t2

Answer 9

what grade are you in? can you understand the above?

Answer 10

10th

Answer 11

then I think the above should be straight forward, right? or do u need me to explain it further?

Answer 12

i understand the multiplication, but please explain further, thanks

Answer 13

which part(s) is/are ambiguous for you? can u point it out please?

Answer 14

to find the cost C

Answer 15

find the cost C as a function of the time t of operation of the factory ?
this part ?

Answer 16

yes

Answer 17

ok forget about the above and I'll give u a simpler example, just bear with me ok?

Answer 18

I can make 5 donuts in t hours, ok? so the function for how many donuts I can make in terms of t hours (time that it takes me to make them ) is:

N = 5 t
after 1 hour I've made 5 donuts
after 2 hours I've made 5*2 = 10 donuts
after 7 hours I've made 5*7 = 35 donuts

is the above clear?

Answer 19

yes

Answer 20

ok now to the next part, btw the above equation can be written as is N(t) = 5*t

Answer 21

The cost C for me to make N number of donuts can be given by this formula

C = $2 + 3N in dollars
$2 are initial costs for gas burner running all the time

so cost of 1 donut = 2+3 = $5
2 donuts ==> 2 + 6 = $8
5 donuts ==> 2 + 15 = $17

do u understand this part?

Answer 22

yes

Answer 23

now they want you to tell them the function of the Cost in terms of the time, you have the formula for the Cost
C(N) = 2 + 3N
and you have the formula of N in terms of time
N(t) = 5t where t is in hours

Then all I have to do is find C(t) by replacing each N in the C(N) formula by its N(t) equivalent, i.e.

C(t) = 2 + 3 (N) but N = 5t, so
C(t) = 2 + 3 (5t) = 2 + 15t

this means the cost of making dounts after 1 hour is 2+15 = $17
after 2 hours ==> 2 + 30 = $32
and so on..

how does that sound?

Answer 24

:) I think i understand what you are saying

Answer 25

their example is a bit more complex because it got t squared and higher initial costs
my example is silly but it conveys the same point
cheers

Answer 26

Thank you very much i think i understand your explanation better. Thanks for your time.

Answer 27

that's ok, yw