Question 1192479
.
The cost function for a container company is c(x)=10x+30 and the revenue function is r(x)=-x^2+24x 
where x is the number of containers sold in thousand. 
(a) Determine the profit function for the number of containers sold. 
(a) Then determine the number of containers sold that maximizes profit
I got P(x)=-x^2-8x-30 and the x would be -4 but that negative confuses me how do you sell -4 000 contains?
~~~~~~~~~~~~~~~~~~



            The formula for the profit function  P(x) = -x^2 - 8x - 30,  which you  " got " 

            and to which you refer,  is wrong,  incorrect and absurdist.



<pre>
The correct formula for the profit is

    P = Revenue - Cost,

or

    P(x) = (-x^2 + 24x) - (10x + 30) = -x^2 + 14x - 30.


It is the  <U>ANSWER</U>  to question (a).



To get the number of containers that maximizes the profit, use the formula

    {{{x[max]}}} = {{{-b/(2a)}}},

where "a" is the coefficient of the profit function at x^2 and b is the coefficient at x.



In your case,  a= -1, b= 14;  therefore  

    {{{x[max]}}} = {{{-14/(2*(-1))}}} = {{{14/2}}} = 7.


Thus the number of containers that maximizes the profit is 7 thousands.


It is the  <U>ANSWER</U>  to question (b).
</pre>

Solved, explained and completed.


----------------


On finding the maximum/minimum of a quadratic function see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>



Consider these lessons as your textbook, &nbsp;handbook, &nbsp;tutorials and &nbsp;(free of charge) &nbsp;home teacher.

Learn the subject from there once and for all.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


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



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.