SOLUTION: Aki’s Bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.5x^2-0.9x+1.861, where C(x) is in hundreds of dollars.

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Question 1098325: Aki’s Bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.5x^2-0.9x+1.861, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
.
The minimal average cost per bicycle is achieved at 

    x = {{-(-0.9)/(2*0.5)}}} = 0.9, 

which corresponds to 90 bicycles.


Answer.  90 bicycles should be built  per day to minimize the average cost per bicycle.


When you have a quadratic function   y = ax^2 + bx + c   with  a > 0,

it achieves its minimum at   x = .


See the lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

--------------------------------
The formula for the x-value of the
minimum,is:
where


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The shop should build 90 bikes to minimize cost
-------------------------
check:
Here's the plot:

Looks about right,

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