Question

A certain company's main source of income is selling cloth bracelets. The company's annual profit (in thousands of dollars) as a function of the price of a bracelet (in dollars) is modeled by: P(x)=-2x^2+16x-24P(x)=−2x 2 +16x−24P, left parenthesis, x, right parenthesis, equals, minus, 2, x, squared, plus, 16, x, minus, 24 What bracelet price should the company set to earn this maximum profit?

Answer 1

Answer:

8 thousand dollars

Step-by-step explanation:

The company's annual profit (in thousands of dollars) as a function of the price of a bracelet (in dollars) is modeled by: P(x)=-2x^2+16x-24

To find maximum profit , we need to find out the vertex

x coordinate of vertex formula is -b/2a

P(x)=-2x^2+16x-24P(x)=−2x

2

+16x−24

a=-2 and b = 16

x= \frac{-b}{2a}= \frac{-16}{2(-2)} = 4x=

2a

−b

=

2(−2)

−16

=4

Now we plug in 4 for x and find out P(4)

P(x)=-2(4)^2+16(4)-24P(x)=−2(4)

2

+16(4)−24 = 8

So the maximum profit the company can earn is 8 thousand dollars when price = $4

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