Asked by Marysvoice
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.
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.
Answers
Answered by
drwls
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)
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)
Answered by
Marysvoice
How do you get 1.333x+17.697 and 1.333x+0.444+17.253 and (x-0.667)^2+17.53?
Answered by
drwls
By dividing out 0.6 and then completing the square. Check the numbers. They work.
Answered by
Destiny
one of two positive intergers is 5 less than the other. if the product of the two intergers is 24, find the intergers
Answered by
roro
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
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
Answered by
de guzman,magic
can you help me
Answered by
Donatello
Find 2 numbers with a difference of 10 and a product that is a minimum. Find the minimum product.
Answered by
Anonymous
243548696797-
5654353574768
756746
5654353574768
756746
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