SOLUTION: 3. A company is trying to minimize their costs. Their accountant comes up with the formula C = 15x2-18x+24, where C equals the cost and x equals the number of hours a machine runs

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Question 1202457: 3. A company is trying to minimize their costs. Their accountant comes up with the formula C = 15x2-18x+24, where C equals the cost and x equals the number of hours a machine runs to help them achieve this.
What are their break even points?
What value would minimize the cost?

If the machine runs for six hours how much would that cost the company?

If the cost is $500, how long was the machine running for?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
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company is trying to minimize their costs. Their accountant comes up with the formula C = 15x2-18x+24, where C equals the cost and x equals the number of hours a machine runs to help them achieve this.
What are their break even points?
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First question must include attention to profit, or to the difference between revenue and cost, but not enough information for this was in the description.
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
3. A company is trying to minimize their costs. Their accountant comes up with the formula
C = 15x2-18x+24, where C equals the cost and x equals the number of hours a machine runs
to help them achieve this.
(a) What are their break even points?
(b) What value would minimize the cost?
(c) If the machine runs for six hours how much would that cost the company?
(d) If the cost is $500, how long was the machine running for?
~~~~~~~~~~~~~~~~~~~ 

(a)  To answer (a), solve this quadratic equation

        C(x) = 0,  or  15x^2-18x+24 = 0.

     It is standard quadratic equation. Solve it either using the quadratic formula OR 
     using factoring if it works.  According to the meaning of "x", only positive roots are acceptable.


(b)  The value of "x", which minimizes the cost, is   = "  ",
     which gives x-coordinate of the vertex.

     Substitute here b= -18, a= 15 and get  

          =  =  =  = 0.6 hours = 36 minutes.


(c)  To answer (c), substitute x= 6 hours into the formula for C, and get the value.
     It is more than simple exercise.



(d)  To answer (d), you should solve this quadratic equation

        15x^2 -18x + 24 = 500  dollars.


     Again, it is simple mechanical exercise, and you can complete it on your own.

Partly solved; regarding the rest, you have full instructions.

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On finding the maximum/minimum of a quadratic function 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


Consider these lessons as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.
Learn the subject from there once and for all.


/////////////////


Surely and obviously, that wording in this post is far from to be perfect,
so I need to make my own hypotheses about the meaning of used words in this post.

It is so typical for numerous illiterate posts at this forum,
that I just tired to discuss, to edit and/or to disprove them.

Every second post is nonsense or semi-delusions.



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