192k views
3 votes
For the cost function, find the marginal cost at the given production level x. State the units of measurement. (All costs are in dollars.) HINT [See Example 1.] C(x) = 15,000 + 50x + 1,000 x ; x = 100

User Atul Goyal
by
8.1k points

1 Answer

3 votes

Answer:

The marginal cost at the given production level is $49.9.

Explanation:

The marginal cost function is expressed as the first derivative of the total cost function with respect to quantity (x).

We have that the cost function is given by


C(x) = 15000 + 50x + (1000)/(x)

So, we need the derivative and then we’ll need to compute the value x = 100 of the derivative.


C'(x)=(d)/(dx)\left(15000+50x+(1000)/(x)\right)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\C'(x)=(d)/(dx)\left(15000\right)+(d)/(dx)\left(50x\right)+(d)/(dx)\left((1000)/(x)\right)\\\\C'(x)=0+50-(1000)/(x^2)\\\\C'(x)=50-(1000)/(x^2)

When x = 100, the marginal cost is


C'(100)=-(1000)/(100^2)+50\\\\C'(100)=(499)/(10)=49.9

User Pavel Zdenek
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories