Question

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

Answer 1

Answer:

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

Step-by-step 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

$C(x) = 15000 + 50x + \frac{1000}{x}$

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

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

When x = 100, the marginal cost is

$C'(100)=-\frac{1000}{100^2}+50\\\\C'(100)=\frac{499}{10}=49.9$