Math

QuestionFind the break-even point where C(x)=60x+2500C(x)=60x+2500 equals revenue from selling xx bats at \$80 each.

Studdy Solution

STEP 1

Assumptions1. The cost function of producing and selling xx bats is C(x)=60x+2500C(x)=60x+2500 . The selling price per bat is $803. The break-even point is the point where total revenue equals total cost

STEP 2

First, we need to find the revenue function. The revenue is calculated by multiplying the selling price per bat by the number of bats sold.
Revenue=SellingpricetimesNumberofbatsRevenue = Selling\, price \\times Number\, of\, bats

STEP 3

Now, plug in the given values for the selling price and the number of bats to get the revenue function.
Revenue=$80timesxRevenue = \$80 \\times x

STEP 4

The break-even point is the point where total revenue equals total cost. Therefore, we can set the cost function equal to the revenue function and solve for xx.
C(x)=RevenueC(x) = Revenue

STEP 5

Plug in the given functions for cost and revenue.
60x+2500=80x60x +2500 =80x

STEP 6

To solve for xx, we need to isolate xx on one side of the equation. Start by subtracting 60x60x from both sides of the equation.
60x60x+2500=80x60x60x -60x +2500 =80x -60x

STEP 7

implify the equation.
2500=20x2500 =20x

STEP 8

Now, divide both sides of the equation by20 to solve for xx.
250020=20x20\frac{2500}{20} = \frac{20x}{20}

STEP 9

Calculate the value of xx.
x=25020=125x = \frac{250}{20} =125The break-even point for the company is when they sell125 bats.

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