the cost of producing $x$ units of stuffed alligator toys is $c(x)=0.004x^{2}+8x + 7000$. find the marginal…

Explanation:

Step1: Recall marginal - cost formula

The marginal cost function $C'(x)$ is the derivative of the cost function $C(x)$. Given $C(x)=0.004x^{2}+8x + 7000$, using the power - rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$, we have $C'(x)=\frac{d}{dx}(0.004x^{2})+\frac{d}{dx}(8x)+\frac{d}{dx}(7000)$.

Step2: Calculate the derivative of each term

$\frac{d}{dx}(0.004x^{2})=2\times0.004x=0.008x$, $\frac{d}{dx}(8x)=8$, and $\frac{d}{dx}(7000)=0$. So, $C'(x)=0.008x + 8$.

Step3: Evaluate the marginal cost at $x = 1000$

Substitute $x = 1000$ into $C'(x)$. $C'(1000)=0.008\times1000+8$. $C'(1000)=8 + 8=16$.

Answer:

$16$