suppose a widget - making company makes its monthly cost as (c(x)=300x^{2}+400x) and its monthly income as…

suppose a widget - making company makes its monthly cost as (c(x)=300x^{2}+400x) and its monthly income as (i(x)= - 0.6x^{3}+500x^{2}-600x + 900), where (x) is the number of widgets being sold. the profit is the difference between the income and the cost.\nwhat is the profit function, (p(x))?\na. (p(x)=-0.6x^{3}+200x^{2}-1000x + 900)\nb. (p(x)=-0.6x^{3}+200x^{2}-200x + 900)\nc. (p(x)=-0.6x^{3}+1300x^{2}+100x + 900)\nd. (p(x)=-0.6x^{3}+200x^{2}-100x + 900)

suppose a widget - making company makes its monthly cost as (c(x)=300x^{2}+400x) and its monthly income as (i(x)= - 0.6x^{3}+500x^{2}-600x + 900), where (x) is the number of widgets being sold. the profit is the difference between the income and the cost.\nwhat is the profit function, (p(x))?\na. (p(x)=-0.6x^{3}+200x^{2}-1000x + 900)\nb. (p(x)=-0.6x^{3}+200x^{2}-200x + 900)\nc. (p(x)=-0.6x^{3}+1300x^{2}+100x + 900)\nd. (p(x)=-0.6x^{3}+200x^{2}-100x + 900)

Answer

Explanation:

Step1: Recall profit formula

Profit $P(x)=R(x)-C(x)$, where $R(x)$ is revenue and $C(x)$ is cost.

Step2: Substitute given functions

Let $C(x) = 300x^{2}+400x$ and $R(x)=0.6x^{3}+900x^{2}- 300x + 600$. Then $P(x)=(0.6x^{3}+900x^{2}-300x + 600)-(300x^{2}+400x)$.

Step3: Simplify the expression

$P(x)=0.6x^{3}+900x^{2}-300x + 600 - 300x^{2}-400x=0.6x^{3}+(900x^{2}-300x^{2})+(-300x-400x)+600=0.6x^{3}+600x^{2}-700x + 600$.

Answer:

B. $P(x)=0.6x^{3}+600x^{2}-700x + 600$