SOLUTION: there are a few parts to this question and i am not sure where to start. any help is greatly appreciated The cost function for a certain company is C (Q) = 60Q + 300 and the re

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: there are a few parts to this question and i am not sure where to start. any help is greatly appreciated The cost function for a certain company is C (Q) = 60Q + 300 and the re      Log On


   

Question 1153502: there are a few parts to this question and i am not sure where to start. any help is greatly appreciated
The cost function for a certain company is C (Q) = 60Q + 300 and the revenue is given by R = 100Q − 0.5Q2. Recall that profit is Revenue R(Q) minus cost C(Q)è R(Q) - C(Q).
Set up a quadratic equation and
Solve the quadratic equation to find the breakeven output (Q).
What does the second breakeven point indicate?
Is that the output level that maximizes profit for the company?
If not, at what output level (Q) will the company’s profit be a maximum?
Use MS-Excel to find two values of Q (production level) that will create a profit of $300
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The point to start is THIS : 


The cost function    is  C(Q) = 60%2AQ+%2B+300      (given !)


The revenue function is  R(Q) = 100%2AQ+-+0.5Q%5E2  (given !)


The profit function is the difference  


    P(Q) = R(Q) - C(Q) = 100%2AQ-0.5Q%5E2 - %2860%2AQ%2B300%29 = -0.5%2AQ%5E2+%2B+40%2AQ+-+300.


Again, the profit is this quadratic function of Q


    P(Q) = -0.5%2AQ%5E2+%2B+40%2AQ+-+300.


Now, for the break even-point the equation is  P(Q) = 0  (saying "NO PROFIT"), or


    -0.5%2AQ%5E2+%2B+40%2AQ+-+300 = 0.


Thus I setup the basic equation for you.


Now, to answer the first question, you should solve this equation and find its roots.

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

At this point I want to STOP, since you asked to show you how to start.

My post explains it . . .


If you still have questions, do not hesitate ask them.

You may report to the forum about your progress, if you want.


Boldly move forward (!)