SOLUTION: Question one The fixed costs of a company is Kshs 35,000 and the variable cost per unit is Kshs 500. The revenue function for sale of x units is given by . Find; i) Profit f

Question 1142279: Question one
The fixed costs of a company is Kshs 35,000 and the variable cost per unit is Kshs 500. The revenue function for sale of x units is given by . Find;
i) Profit function
ii) Break even values
iii) The values of x which result in a loss

Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

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

(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)




    


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.

Do not forget to post your "THANKS" to me.

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