Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
-Use the revenue and cost functions to write the profit function from producing and selling $x$ binoculars.
A) $P ( x ) = 2 x + 1500$
B) $P ( x ) = 4 x + 1500$
C) $\mathrm { P } ( \mathrm { x } ) = 2 \mathrm { x } - 1500$
D) $\mathrm { P } ( \mathrm { x } ) = 4 \mathrm { x } - 1500$

Question

Quizplus · Accepted Answer

The profit function, $P(x)$, is defined as the revenue function, $R(x)$, minus the cost function, $C(x)$. Therefore, if $R(x) = a\cdot x$ and $C(x) = b + a\cdot x$, where $b$ is the fixed cost, then $P(x) = R(x) - C(x) = a\cdot x - (b + a\cdot x) = a\cdot x - b$. The correct option, $P(x) = 2x - 1500$, reflects this relationship, indicating a linear profit function where the profit increases by 2 units for every additional unit sold, after accounting for a fixed cost of 1500.

Given the Cost Function, C(x), and the Revenue Function, R(x) xxx

Given the Cost Function, C(x), and the Revenue Function, R(x) $x$