total profit is defined as total revenue, $r(x)$, minus total cost, $c(x)$, and is given by the function…

total profit is defined as total revenue, $r(x)$, minus total cost, $c(x)$, and is given by the function $p(x)=r(x)-c(x)$. given $r(x)=54x - 0.4x^{2}$ and $c(x)=5x + 13$, find each of the following. a) $p(x)$ b) $r(70)$, $c(70)$, and $p(70)$ $p(x)=-0.4x^{2}+54x - 13$ (type in descending powers of $x$.) $r(70)=$

total profit is defined as total revenue, $r(x)$, minus total cost, $c(x)$, and is given by the function $p(x)=r(x)-c(x)$. given $r(x)=54x - 0.4x^{2}$ and $c(x)=5x + 13$, find each of the following. a) $p(x)$ b) $r(70)$, $c(70)$, and $p(70)$ $p(x)=-0.4x^{2}+54x - 13$ (type in descending powers of $x$.) $r(70)=$

Answer

Explanation:

Step1: Find $P(x)$

Given $P(x)=R(x)-C(x)$, $R(x) = 51x-0.4x^{2}$ and $C(x)=5x + 13$. Substitute the functions: $P(x)=(51x-0.4x^{2})-(5x + 13)=-0.4x^{2}+(51x - 5x)-13=-0.4x^{2}+46x-13$

Step2: Find $R(70)$

Substitute $x = 70$ into $R(x)$: $R(70)=51\times70-0.4\times70^{2}=51\times70-0.4\times4900=3570 - 1960=1610$

Step3: Find $C(70)$

Substitute $x = 70$ into $C(x)$: $C(70)=5\times70+13=350 + 13=363$

Step4: Find $P(70)$

Substitute $x = 70$ into $P(x)$: $P(70)=-0.4\times70^{2}+46\times70-13=-0.4\times4900+3220-13=-1960+3220 - 13=1247$

Answer:

$P(x)=-0.4x^{2}+46x - 13$ $R(70)=1610$ $C(70)=363$ $P(70)=1247$