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 $679.\n\n$r(x)=25x$\nthe revenue function.\n\n$c(x)=18x + 455$\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 $679.\n\n$r(x)=25x$\nthe revenue function.\n\n$c(x)=18x + 455$\nthe cost function.

Answer

Explanation:

Step1: Define profit function

Profit $P(x)=R(x)-C(x)$. Substitute $R(x) = 25x$ and $C(x)=18x + 455$ into the formula. $P(x)=25x-(18x + 455)=25x-18x-455 = 7x-455$

Step2: Solve for x when $P(x)=679$

Set $P(x)=679$, so we have the equation $7x-455 = 679$. Add 455 to both sides: $7x=679 + 455$. $7x=1134$. Divide both sides by 7: $x=\frac{1134}{7}=162$

Answer:

The profit function is $P(x)=7x - 455$ and 162 units must be produced to make a profit of $679$.