I need some help on this equation:
$x\;$: Output Quantity
$CF\;$: Cost Function:
$CF(x)=5000+100x-\frac{x^2}{24}\;\leftrightarrow\;0\leq x\leq1600$
Now, I've already noticed that it sounds a litte bit strange, but, how can I calculate and find the maximum point of the output production quantity, instead of calculating the maximum marginal or total revenue in this situation? Please, show me how to approach and solve this problem.
Thank you for reading this and helping us all about…
PS: The problem asks for the maximum production point here.
Best Answer
With $0\leq x\leq 1600$, the maximum value for the "output quantity" $x$ is $1600$.
At this point the "total cost" is falling, which seems a little strange.
As you say in a comment on the question, you can set the derivative of the cost function to $0$ to help trying to find a turning point in the cost function, and this will give you $x=1200$. Since the cost function is and upside down parabobla, the is the production point which maximises the cost (which is $65000$ at this point).
It turns out this is what you were asked for. Google Translate sends "olduğu üretim miktarı kaçtır?" to "What is the amount of production?" and "maliyetin en yüksek (maksimum)" to "cost is highest (maximum)"