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 make a profit of $567.\n\n$r(x)=18x$\nthe revenue function.\n\n$c(x)=9x + 423$\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 make a profit of $567.\n\n$r(x)=18x$\nthe revenue function.\n\n$c(x)=9x + 423$\nthe cost function.

Answer

Explanation:

Step1: Find the profit function

The profit function $P(x)$ is given by $P(x)=R(x)-C(x)$. Substitute $R(x) = 18x$ and $C(x)=9x + 423$ into the formula. $P(x)=18x-(9x + 423)=18x-9x-423 = 9x-423$

Step2: Solve for x when $P(x)=567$

Set $P(x)=567$, so we have the equation $9x-423 = 567$. Add 423 to both sides of the equation: $9x-423+423=567 + 423$, which simplifies to $9x=990$. Divide both sides by 9: $x=\frac{990}{9}=110$.

Answer:

The profit function is $P(x)=9x - 423$ and 110 units must be produced to make a profit of $567$.