Math Snap

STEP 1

Assumptions1. The cost function is $C=55x+450$
. The revenue function is $R=80x$
3. To break even, the revenue must be equal to or greater than the cost

STEP 2

First, we need to find the break-even point. This is where the cost equals the revenue.
$$C = R$$

STEP 3

Now, plug in the given functions for the cost and revenue to find the break-even point.
$$55x +450 =80x$$

STEP 4

Rearrange the equation to isolate $x$ on one side.
$$80x -55x =450$$

STEP 5

implify the equation to find the value of $x$.
$$25x =450$$

STEP 6

Divide both sides by25 to solve for $x$.
$$x = \frac{450}{25}$$

STEP 7

Calculate the value of $x$.
$$x = \frac{450}{25} =18$$

So, the product will at least break even when $x \geq18$. Therefore, the interval is $[18, \infty)$.
The product will at least break even when18 or more units are produced.