SOLUTION: Determine the number of units x that produce a maximum revenue, in dollars, for the given revenue function. R(x) = 312x − 0.2x2 x = units Determine the maximum revenue

Algebra ->  Inequalities -> SOLUTION: Determine the number of units x that produce a maximum revenue, in dollars, for the given revenue function. R(x) = 312x − 0.2x2 x = units Determine the maximum revenue      Log On


   

Question 1129343: Determine the number of units x that produce a maximum revenue, in dollars, for the given revenue function.
R(x) = 312x − 0.2x2
x = units
Determine the maximum revenue.____$
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

R%28x%29+=+312x+-0.2x%5E2
it’s parabola, and max is at vertex; write it in vertex form
R%28x%29+=++-0.2x%5E2%2B312x...eliminate decimal, multiply by 10
R%28x%29+=++-2x%5E2%2B3120x
R%28x%29+=++-2%28x%5E2-1560x%29
R%28x%29+=++-2%28x%5E0.2-1560x%2Bb%5E2%29-2%28-1560%5E2%29-> 2ab=1560,a=1=>b=1560%2F2=780
R%28x%29+=++-2%28x%5E2-1560x%2B780%5E2%29-2%28-780%5E2%29
R%28x%29+=++-2%28x-780%29%5E2%2B1216800
vertex is at
(780, 121680)
x+=780 units
Determine the maximum revenue.121680$

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the number of units x that produce a maximum revenue, in dollars, for the given revenue function.
R(x) = 312x − 0.2x2
x = units
Determine the maximum revenue.____$ 
You don't have to do all of that. I would TOTALLY IGNORE all that the other person did, as it's TOTALLY UNNECESSARY work. For what? For NOTHING!!

Unless, of course you wish to learn how to complete the square. Still, I wouldn't use a function like this to complete the square on.



The units that produce a maximum revenue is at the point where matrix%281%2C3%2C+x%2C+%22=%22%2C-+b%2F%282a%29%29

This becomes: 

Now, the maximum revenue is: R(780), so just SUBSTITUTE and calculate!

That's all!! Nothing more, nothing less!!