The question is-

Aki’s Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x) = 0.6x^2-0.8x+10.618, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?

I think- the function, C(x), gives the average cost when x hundred bicycles are made. This is my quadratic function right? Where the coefficient of x^2 is positive? Then the minimum value will be at the vertex?

So I need the form y=a(x-h)^2+k to get my minimum value- x=h.

Now, I need to separate the constant part from the remainder of the function and factor the coefficient of x^2 from the terms containing x. (I am supposed to round to three decimal places if needed.

C(x) = 0.6x^2-0.8+10.618

Now I am lost

C(x)= 0.6 (x^2-?.??x)+10.618

Where does this equation come from?

With that I can complete the square by taking half the answer and squaring it.

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1. Yes, C(x) is the quadratic cost function, and the minimum is at the vertex.

C(x) = 0.6x^2-0.8x+10.618
= 0.6(x^2 - 1.333x + 17.697)
= 0.6 (x^2 - 1.333x +0.444 + 17.253)
= 0.6 [(x- 0.667)^2 + 17.53]
There is a minimum average cost when x = 0.667 hundred bikes (or 67 bikes).

These must be pretty expensive bikes. The minimum cost is 10.35 hundred dollars (\$1035)

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posted by drwls
2. How do you get 1.333x+17.697 and 1.333x+0.444+17.253 and (x-0.667)^2+17.53?

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3. By dividing out 0.6 and then completing the square. Check the numbers. They work.

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posted by drwls
4. one of two positive intergers is 5 less than the other. if the product of the two intergers is 24, find the intergers

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posted by Destiny
5. x*y = 24
y = x - 5 so the equation becomes:
x*(x - 5) = 24
expand: x^2 - 5x - 24 - 0
Factor by sum and product method:
(x - 8)(x + 3) = 0 so x = 8 or x = -3
since the integers are positive, the solution is x = 8, and y = x - 5, so
y = 8 - 5, y = 3
the two integers are 3 and 8

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posted by roro
6. can you help me

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7. Find 2 numbers with a difference of 10 and a product that is a minimum. Find the minimum product.

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8. 243548696797-
5654353574768
756746

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