Question

The price received for a bicycle is given by the equation b = 100 – 10x2, where x is the number of bicycles produced, in millions. It costs the company $60 to make each bicycle. What is the profit function for the company? P = –10x2 – 60x + 100 P = –10x3 + 40x P = – 10x2 + 40 The company recently reduced its production to 1 million bicycles, but maintained its profit of 30 million dollars. What greater number of bicycles had the company previously produced to make the same profit? Round your answer to the nearest tenth. 30 million bicycles

Answer 1

answer:

I.  B. P = –10x3 + 40x

II.  1.3

hope this helps! :o)

Answer 2

The correct option is B) $\rm P = -10x^3+40x$.

1.3 million number of bicycles had the company previously produced to make the same profit.

Step-by-step explanation:

Given :

Price received for a bicycle is,

$b = 100-10x^2$

x is the number of bicycles.

Costs to the company $60 to make each bicycle.

Calculation :

Profit Function = Revenue function - Cost function

$\rm P = x(100-10x^2) - 60(x)$

$\rm P = -10x^3+40x$

Therefore option B) is correct.

Now, to find number of bicycles had the company previously produced to make the same profit we have

$30=-10x^3+40x$

$x^3-4x+3=0$

$x^3-x^2+x^2-x-3x+3=0$

$x^2(x-1)+x(x-1)-3(x-1)=0$

$(x-1)(x^2+x-3)=0$

$x=\dfrac{-1\pm\sqrt{1+12} }{2}$

We take positive,

$x=\dfrac{-1+\sqrt{13} }{2}=1.3$

company recently reduced its production to, x = 1 million bicycles.

Therefore, 1.3 million number of bicycles had the company previously produced to make the same profit.

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