Question

If the cost of manufacturing x items is x^3 + 20x^2 + 90x + 15 , find the marginal cost function and compare the marginal cost at x = 50 and the actual cost of manufacturing the 50th item.

Answer 1

@Meepi can u help?

Answer 2

I did it but my teacher said I got it wrong here is what i did

f’(x) = x^3 + 20x^2 + 90x + 15
= 3x^2 + 40x + 90
50^3 + 20(500^2 + 90(50) + 15 = 125015
49^3 + 20(49)^2 + 90(49) + 15 = 1082474
c(50) – c(49) = 42541
f’(x) = 3x^2 + 40 + 90 = 24590
actual cost : 42541
marginal cost: 24590

Answer 3

She said to Find c'(50) and recalculate c(50)-c(49).

Answer 4

Cost is c(x) = \(\Large x^3 + 20x^2 + 90x + 15\)
Marginal cost c'(x) = \(\Large 3x^2 + 40x + 90\)

Marginal cost at x = 50 is c'(50) =
\[3(50)^2+40*50+90 = 3*2500 + 2090 = 9590\]
Actual cost of the 50'th item:
c(50) - c(49) = \(50^3 + 20(50)^2 + 90*50+15 - 49^3 - 20(49)^2 - 90*49 - 15\)
= 9421

Answer 5

Do you have to calculate this by hand?

Answer 6

ok i see where i did my mistake