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Lyrx [107]
2 years ago
15

A bicycle manufacturer uses the given expression to model the monthly profit from sales of a new model of bicycle, where x is th

e selling price of one bicycle, in dollars. At what selling prices for the bicycle will the manufacturer make neither a profit nor a loss?
Mathematics
1 answer:
forsale [732]2 years ago
8 0

Answer:

The manufacturer will have no profit or loss when the selling price equals $200 or $100.

Step-by-step explanation:

The expression to model the monthly profit from sales of a new model of bicycle is

-x^2 + 300x -20,000

Let

f(x) -----> the monthly profit in dollars

x -----> s the selling price of one bicycle in dollars

f(x)= -x^{2}+300x-20,000

we know that

The manufacturer will make no profit nor a loss when the profit is equal to zero

so

f(x)=0

-x^{2}+300x-20,000=0

Multiply by -1 both sides

x^{2}-300x+20,000=0

The formula to solve a quadratic equation of the form ax^{2} +bx+c=0 is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

a=1\\b=-300\\c=20,000

substitute in the formula

x=\frac{300(+/-)\sqrt{-300^{2}-4(1)(20,000)}}{2(1)}

x=\frac{300(+/-)\sqrt{10,000}}{2}

x=\frac{300(+/-)100}{2}

x=\frac{300(+)100}{2}=200

x=\frac{300(-)100}{2}=100

therefore

The manufacturer will have no profit or loss when the selling price equals $200 or $100.

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