Question

the cost and revenue functions c and r are shown for producing and selling x items. determine the values of x for which
(a) ( r(x) = c(x) ) (the company breaks even)
(b) ( r(x) < c(x) ) (the company experiences a loss)
(c) ( r(x) > c(x) ) (the company makes a profit)
part 1 of 3
(a) the value of x for which ( r(x) = c(x) ) is {800}.

Explanation:

Step1: Identify break-even x-value

The intersection of $R(x)$ and $C(x)$ is at $x=800$.

Step2: Find loss region (R<C)

$C(x)$ is above $R(x)$ when $x<800$.

Step3: Find profit region (R>C)

$R(x)$ is above $C(x)$ when $x>800$.

Answer:

(a) $\{800\}$
(b) All real numbers $x$ where $0 < x < 800$
(c) All real numbers $x$ where $x > 800$