the revenue for a business, as a function of units produced, x, is shown below by r(x). c(x) represents the…

the revenue for a business, as a function of units produced, x, is shown below by r(x). c(x) represents the cost of producing x units. calculate the profit function and then determine how many units must be produced for the business to break even.\n\n$r(x)=16x$\nthe revenue function.\n\n$c(x)=3x + 741$\nthe cost function.

the revenue for a business, as a function of units produced, x, is shown below by r(x). c(x) represents the cost of producing x units. calculate the profit function and then determine how many units must be produced for the business to break even.\n\n$r(x)=16x$\nthe revenue function.\n\n$c(x)=3x + 741$\nthe cost function.

Answer

Explanation:

Step1: Define profit function

The profit function $P(x)$ is given by $P(x)=R(x)-C(x)$. Substitute $R(x) = 16x$ and $C(x)=3x + 741$ into the formula. $P(x)=16x-(3x + 741)$ $P(x)=16x-3x-741$ $P(x)=13x-741$

Step2: Find break - even point

At the break - even point, profit is zero, i.e., $P(x)=0$. Set $13x-741 = 0$. Add 741 to both sides: $13x=741$. Divide both sides by 13: $x=\frac{741}{13}=57$.

Answer:

The profit function is $P(x)=13x - 741$ and the number of units to break even is 57.