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QuestionFind cost C(x)=28750+1900xC(x)=28750+1900x, revenue R(x)=2525xR(x)=2525x, and the break-even point. Explain its meaning.

Studdy Solution

STEP 1

Assumptions1. The cost function is C(x)=28750+1900xC(x)=28750+1900x . The revenue function is R(x)=2525xR(x)=2525x
3. We need to find the break-even point, which is the point where cost equals revenue

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

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

STEP 8

Now that we have the value of xx, we can find the break-even point by substituting xx into either the cost function or the revenue function.
C(46)=28750+1900×46C(46) =28750 +1900 \times46

STEP 9

Calculate the value of C(46)C(46).
C(46)=$115,500C(46) = \$115,500

STEP 10

The break-even point is therefore (46, \$115,500). This means that for46 sold-out performances, both cost and revenue are \$115,500.

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