QuestionFind the intervals where production of $x$ units of wire breaks even, given $C=55x+450$ and $R=80x$ .

Studdy Solution

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 $x$ .
$x = \frac{450}{25} =18$

STEP 8

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.

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QuestionFind the intervals where production of $x$ units of wire breaks even, given $C=55x+450$ and $R=80x$ .

Studdy Solution

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 $x$ .
$x = \frac{450}{25} =18$

STEP 8

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.

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QuestionFind the intervals where production of xxx units of wire breaks even, given C=55x+450C=55x+450C=55x+450 and R=80xR=80xR=80x.

Studdy Solution

STEP 1

Assumptions1. The cost function is C=55x+450C=55x+450C=55x+450 . The revenue function is R=80xR=80xR=80x3. 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=RC = RC=R

STEP 3

Now, plug in the given functions for the cost and revenue to find the break-even point.55x+450=80x55x +450 =80x55x+450=80x

STEP 4

Rearrange the equation to isolate xxx on one side.80x−55x=45080x -55x =45080x−55x=450

STEP 5

implify the equation to find the value of xxx.25x=45025x =45025x=450

STEP 6

Divide both sides by25 to solve for xxx.x=45025x = \frac{450}{25}x=25450​

STEP 7

Calculate the value of xxx.x=45025=18x = \frac{450}{25} =18x=25450​=18

STEP 8

So, the product will at least break even when x≥18x \geq18x≥18. Therefore, the interval is [18,∞)[18, \infty)[18,∞).The product will at least break even when18 or more units are produced.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the intervals where production of $x$ units of wire breaks even, given $C=55x+450$ and $R=80x$ .

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

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

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

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

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

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

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.