QuestionLet $x$ be sold-out performances.
a. Cost function: $C(x)=28750+1900x$ . b. Revenue function: $R(x)=2525x$ . c. Find break-even point and explain its meaning. Choose A, B, or C to describe it.

Studdy Solution

STEP 1

Assumptions1. The cost function is given by $C(x)=28750+1900x$ . The revenue function is given by $R(x)=2525x$
3. The break-even point is the point where cost equals revenue, i.e., $C(x) = R(x)$

STEP 2

To find the break-even point, we need to set the cost function equal to the revenue function and solve for $x$ .
$C(x) = R(x)$

STEP 3

Substitute the given cost and revenue functions into the equation.
$28750+1900x =2525x$

STEP 4

Rearrange the equation to isolate $x$ terms on one side.
$252x -1900x =28750$

STEP 5

implify the left side of the equation.
$625x =28750$

STEP 6

olve for $x$ by dividing both sides of the equation by625.
$x = \frac{28750}{625}$

STEP 7

Calculate the value of $x$ .
$x =46$

STEP 8

Substitute $x =46$ into either the cost function or the revenue function to find the break-even revenue/cost.
$C(46) = R(46) =2525 \times46$

STEP 9

Calculate the break-even revenue/cost.
$C(46) = R(46) = \$115,150$ The break-even point is (46, \$115,150). This means that for46 sold-out performances, both cost and revenue are \$115,150.

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QuestionLet $x$ be sold-out performances.
a. Cost function: $C(x)=28750+1900x$ . b. Revenue function: $R(x)=2525x$ . c. Find break-even point and explain its meaning. Choose A, B, or C to describe it.

Studdy Solution

STEP 1

Assumptions1. The cost function is given by $C(x)=28750+1900x$ . The revenue function is given by $R(x)=2525x$
3. The break-even point is the point where cost equals revenue, i.e., $C(x) = R(x)$

STEP 2

To find the break-even point, we need to set the cost function equal to the revenue function and solve for $x$ .
$C(x) = R(x)$

STEP 3

Substitute the given cost and revenue functions into the equation.
$28750+1900x =2525x$

STEP 4

Rearrange the equation to isolate $x$ terms on one side.
$252x -1900x =28750$

STEP 5

implify the left side of the equation.
$625x =28750$

STEP 6

olve for $x$ by dividing both sides of the equation by625.
$x = \frac{28750}{625}$

STEP 7

Calculate the value of $x$ .
$x =46$

STEP 8

Substitute $x =46$ into either the cost function or the revenue function to find the break-even revenue/cost.
$C(46) = R(46) =2525 \times46$

STEP 9

Calculate the break-even revenue/cost.
$C(46) = R(46) = \$115,150$ The break-even point is (46, \$115,150). This means that for46 sold-out performances, both cost and revenue are \$115,150.

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QuestionLet xxx be sold-out performances. a. Cost function: C(x)=28750+1900xC(x)=28750+1900xC(x)=28750+1900x. b. Revenue function: R(x)=2525xR(x)=2525xR(x)=2525x. c. Find break-even point and explain its meaning. Choose A, B, or C to describe it.

Studdy Solution

STEP 1

Assumptions1. The cost function is given by C(x)=28750+1900xC(x)=28750+1900xC(x)=28750+1900x . The revenue function is given by R(x)=2525xR(x)=2525xR(x)=2525x3. The break-even point is the point where cost equals revenue, i.e., C(x)=R(x)C(x) = R(x)C(x)=R(x)

STEP 2

To find the break-even point, we need to set the cost function equal to the revenue function and solve for xxx.C(x)=R(x)C(x) = R(x)C(x)=R(x)

STEP 3

Substitute the given cost and revenue functions into the equation.28750+1900x=2525x28750+1900x =2525x28750+1900x=2525x

STEP 4

Rearrange the equation to isolate xxx terms on one side.252x−1900x=28750252x -1900x =28750252x−1900x=28750

STEP 5

implify the left side of the equation.625x=28750625x =28750625x=28750

STEP 6

olve for xxx by dividing both sides of the equation by625.x=28750625x = \frac{28750}{625}x=62528750​

STEP 7

Calculate the value of xxx.x=46x =46x=46

STEP 8

Substitute x=46x =46x=46 into either the cost function or the revenue function to find the break-even revenue/cost.C(46)=R(46)=2525×46C(46) = R(46) =2525 \times46C(46)=R(46)=2525×46

STEP 9

Calculate the break-even revenue/cost.C(46)=R(46)=$115,150C(46) = R(46) = \$115,150C(46)=R(46)=$115,150The break-even point is (46, \$115,150). This means that for46 sold-out performances, both cost and revenue are \$115,150.

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Studdy solves anything!

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

QuestionLet $x$ be sold-out performances.
a. Cost function: $C(x)=28750+1900x$ . b. Revenue function: $R(x)=2525x$ . c. Find break-even point and explain its meaning. Choose A, B, or C to describe it.

Assumptions1. The cost function is given by $C(x)=28750+1900x$ . The revenue function is given by $R(x)=2525x$
3. The break-even point is the point where cost equals revenue, i.e., $C(x) = R(x)$

To find the break-even point, we need to set the cost function equal to the revenue function and solve for $x$ .
$C(x) = R(x)$

Substitute the given cost and revenue functions into the equation.
$28750+1900x =2525x$

Rearrange the equation to isolate $x$ terms on one side.
$252x -1900x =28750$

implify the left side of the equation.
$625x =28750$

olve for $x$ by dividing both sides of the equation by625.
$x = \frac{28750}{625}$

Calculate the value of $x$ .
$x =46$

Substitute $x =46$ into either the cost function or the revenue function to find the break-even revenue/cost.
$C(46) = R(46) =2525 \times46$

Calculate the break-even revenue/cost.
$C(46) = R(46) = \$115,150$ The break-even point is (46, \$115,150). This means that for46 sold-out performances, both cost and revenue are \$115,150.