question 25 of 25\nsuppose a publishing company estimates that its monthly cost is $c(x)=600x^{2}+300x$ and…

question 25 of 25\nsuppose a publishing company estimates that its monthly cost is $c(x)=600x^{2}+300x$ and its monthly revenue is $r(x)= - 0.4x^{3}+700x^{2}-600x + 500$, where $x$ is in thousands of books sold. the profit is the difference between the revenue and the cost.\nwhat is the profit function, $p(x)$?\na. $p(x)=0.4x^{3}+100x^{2}-900x + 500$\nb. $p(x)=-0.4x^{3}+100x^{2}-900x + 500$\nc. $p(x)=-0.4x^{3}+1300x^{2}-300x + 500$\nd. $p(x)=0.4x^{3}-100x^{2}+900x - 500$

question 25 of 25\nsuppose a publishing company estimates that its monthly cost is $c(x)=600x^{2}+300x$ and its monthly revenue is $r(x)= - 0.4x^{3}+700x^{2}-600x + 500$, where $x$ is in thousands of books sold. the profit is the difference between the revenue and the cost.\nwhat is the profit function, $p(x)$?\na. $p(x)=0.4x^{3}+100x^{2}-900x + 500$\nb. $p(x)=-0.4x^{3}+100x^{2}-900x + 500$\nc. $p(x)=-0.4x^{3}+1300x^{2}-300x + 500$\nd. $p(x)=0.4x^{3}-100x^{2}+900x - 500$

Answer

Explanation:

Step1: Recall profit - revenue - cost formula

The profit function $P(x)$ is given by $P(x)=R(x)-C(x)$.

Step2: Substitute the given functions

We have $R(x)= - 0.4x^{3}+700x^{2}-600x + 500$ and $C(x)=600x^{2}+300x$. So $P(x)=(-0.4x^{3}+700x^{2}-600x + 500)-(600x^{2}+300x)$.

Step3: Distribute the negative sign

$P(x)=-0.4x^{3}+700x^{2}-600x + 500 - 600x^{2}-300x$.

Step4: Combine like - terms

For the $x^{2}$ terms: $700x^{2}-600x^{2}=100x^{2}$. For the $x$ terms: $-600x-300x=-900x$. So $P(x)=-0.4x^{3}+100x^{2}-900x + 500$.

Answer:

B. $P(x)=-0.4x^{3}+100x^{2}-900x + 500$