Question 1142279
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In this post, you missed (lost) the key part: the expression for the revenue function.


Without it, the problem CAN NOT be solved.



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<U>Comment from student</U> : the revenue function by R(x)=5000x - 100x2.
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<U>My response</U> : OK.  Then


<pre>
(i)  The profit function is


     P(x) = R(x) - C(x) = (5000x - 100x^2) - (35000 + 500x) 



(ii)  Break even value.


      To find it, solve this quadratic equation


          P(x) = R(x) - C(x) = 0,  which is the same as


          (5000x - 100x^2) - (35000 + 500x) = 0.


       Simplify the left side and write the equation in the standard form;

       then apply the quadratic formula  //or factoring, if it works// to find the root.


       The root of the quadratic equation will be your answer.



(iii) I am attaching the plot of the quadratic function for profit P(x)




    {{{graph( 500, 500, -10, 50, -1000, 20000,
              (5000x - 100x^2) - (35000 + 500x)
    )}}}


Plot  of the profit function P(x) = (5000x - 100x^2) - (35000 + 500x).



In the plot, you see the roots.  The profit is positive where the parabola is over the x-axis.

The profit is negative (= loss) where the parabola is BELOW the x-axis.


This plot is your GUIDE to complete the solution on YOUR OWN.
</pre>


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