Question

The total cost in dollars to produce q units of a product is C(q). Fixed costs are $13000 . The marginal cost is C'(q)=0.006q^2-q+50.

Estimate C(170) , the total cost to produce 170 units.Find the value of C'(170). Then combine these to find C(171).

I found the value of C'(170) but am unsure of how to get the original equation to help solve the rest of the problem.

Answer 1

I am assuming C'(q) does not mean derivative

Answer 2

it does.

Answer 3

\[(\int\limits_0^{170} \left(0.006 q^2-q+50\right) \, dq\]

Answer 4

so I don't need to find the original function?

Answer 5

you are not given C[q]

Answer 6

but I don't need to solve for it?

Answer 7

you need to integrate then add it to fix costs of 13,000

Answer 8

I got 3876 from integration

Answer 9

i got 3876 as well. then i find the derivative.and for 171, add to 13000?

Answer 10

integrate up to 171 to get c(171)

Answer 11

after i integrate, add 13000?

Answer 12

Yes

Answer 13

i might have integrated wrong then because I got 9070.078 after adding 13000.

Answer 14

are you in diff eq class

Answer 15

no im in calc 1.

Answer 16

ok, good

Answer 17

i did the same steps for the next problem but i keep getting the first and last part worng but the middle correct.

Answer 18

wrong*

Answer 19

C[170]=16876
is this right?

Answer 20

Then the question says add C'(170) which I found to be 53.4 totalling 16929.40. Is that correct according to your answers?

Answer 21

yes that it correct. how'd you get that value exactly?

Answer 22

\[\int\limits_0^{170} \left(0.006 q^2-q+50\right) \, dq\]=3876

3876 + 13000=16876

add C'[170]=53.4
16876+53.4=16929.40

Answer 23

I plugged 170 into the C'(q) equation. That gave me 53.4(well 53.40 in dollars that is). If you add that amount to C(170) it basically increases you to how much it would cost to produce 171 units. Now if you plugged C'(171) in and added that amount to 16929.40 it would give the amount of dollars to produce 172 units. See what we're doing? It's like voodoo! LOL

Answer 24

oh that's the part I missed! Thanks so much for helping me out& posting really, I appreciate it a lot!

Answer 25

Welcome of course!

Answer 26

:)