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)=60x - 0.4x² and c(x)=4x + 13, find each of the following. a) p(x) b) r(100), c(100), and p(100) p(x)= (type in descending powers of x.)

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)=60x - 0.4x² and c(x)=4x + 13, find each of the following. a) p(x) b) r(100), c(100), and p(100) p(x)= (type in descending powers of x.)

Answer

Explanation:

Step1: Substitute R(x) and C(x) into P(x) formula

$P(x)=R(x)-C(x)=(60x - 0.4x^{2})-(4x + 13)$

Step2: Remove parentheses and combine like - terms

$P(x)=60x - 0.4x^{2}-4x - 13=-0.4x^{2}+(60x - 4x)-13=-0.4x^{2}+56x - 13$

Step3: Calculate R(100)

$R(100)=60\times100-0.4\times100^{2}=6000 - 0.4\times10000=6000 - 4000 = 2000$

Step4: Calculate C(100)

$C(100)=4\times100 + 13=400+13 = 413$

Step5: Calculate P(100)

$P(100)=-0.4\times100^{2}+56\times100 - 13=-0.4\times10000+5600 - 13=-4000+5600 - 13 = 1587$

Answer:

a) $P(x)=-0.4x^{2}+56x - 13$ b) $R(100)=2000$, $C(100)=413$, $P(100)=1587$