please help!

[sandra2223]

I just dont get it, can someone please help me.

The profit function for a certain item is p(x)= -.05x^2+100x+1000
How many units should be produced and sold to maximize profit? What is the maximum profit?

 

[galactus]

Differentiate your profit function, set to 0 and solve for x.

Where x is the number of units. Then, upon finding that, plug it back into your profit function to find the max profit.

 

[sandra2223]

i got 100 as the units produced, is that right?

i still cant figure out the maximum profit.

 

[galactus]

It's not 100. It's x=1000.

They give you the profit formula. As I said before, plug it in.

 

[sandra2223]

i got maximum profit of 1,100, is that right? i appreciate your help.

 

[galactus]

No. Plugging x=1000 into the formula gives an answer much more than 1100.

 

[sandra2223]

the formula is -0.1x+100, right? or the orginal formula i started out with?

 

[BigGlenntheHeavy]

\(\displaystyle P(x) \ = \ -.05x^{2}+100x+1000\)

\(\displaystyle P'(x) \ = \ 100-.1x, \ setting \ slope \ to \ zero \ gives \ x \ = \ 1000.\)

\(\displaystyle P(1000) \ = \ 51,000\)


\(\displaystyle See \ graph.\)

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