Question

The cost of manufacturing x items is given by C(x) = 0.02x^2 + 20x + 1800. Find the marginal cost function. Compuare the marginal cost at x = 20 to the actual cost of producing the 20th item.

Answer 1

This is what i did but my teacher says it wrong.

C(x) = 0.02x^2 + 20x + 1800
C’(x) = 0.04x + 20
C’(20) = 0.04(20) + 20 = 20.8 so this will be the marginal cost at x = 20
Acutal cost of the 20th item : c(20) - c(19) = 0.02(20^2) + 20(20) + 1800 – 0.02(19)^2 + 20(19) + 1800 = 4380.78

Answer 2

@agent0smith can u help?

Answer 3

c(20)-c(19) = 2208 - 2187,22 = 20.78
it is just one algebraic mistake

Answer 4

okay thanks so thats the marginal cost?

Answer 5

no! u already got the amrginal cost
"C’(20) = 0.04(20) + 20 = 20.8 so this will be the marginal cost at x = 20 "

Answer 6

ohh okay so what do i do next?

Answer 7

u wrote this
"Acutal cost of the 20th item : c(20) - c(19) = 0.02(20^2) + 20(20) + 1800 – 0.02(19)^2 + 20(19) + 1800 = 4380.78 "
i m telling u that part is wrong with algebraic mistakes

Answer 8

okay

Answer 9

so you're saying in that its where i made my sitake?

Answer 10

yes

Answer 11

i made that calculations and i got

c(20)-c(19) = 2208 - 2187,22 = 20.78

Answer 12

so how about the actual cost?

Answer 13

@Loser66 so how would i find the actual cost? should i just substitute 20 into the first problem?

Answer 14

sorry friend, I totally lost you in this question. I don't get why you subtract C(20 ) -C(19)

Answer 15

to get the marginal cost? i'm so confused :/

Answer 16

@ganeshie8

Answer 17

@RadEn

Answer 18

@mathstudent55

Answer 19

I know why don't get you, hihi, it's economic problem. hand off, friend. never known before

Answer 20

hi again
so what part u dont understand
i think the problem is done

Answer 21

i'm trying to figure it out what is the actual cost is? since we already found marginal cost

Answer 22

u have the marginal cost
C’(x) = 0.04x + 20
C’(20) = 0.04(20) + 20 = 20.8
and the actual cost of producing the 20th item.
c(20)-c(19) = 2208 - 2187,22 = 20.78
the problem says that u must compare them and u can can see they r very close

Answer 23

how how do i do that?

Answer 24

how to do what? compare them?
20.8 is very close to 20.78 u dont need to do anymore

Answer 25

okay thanks