SOLUTION: The profit function for a computer company is given by P(x)=&#8722;x^2+22x&#8722;18 where x is the number of units produced (in thousands) and the profit is in thousand of dollars.

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Question 912653: The profit function for a computer company is given by P(x)=−x^2+22x−18 where x is the number of units produced (in thousands) and the profit is in thousand of dollars.
a) Determine how many (thousands of) units must be produced to yield maximum profit. Determine the maximum profit.
MY ANSWER:(thousands of) units = 11
MY ANSWER: maximum profit = 345 thousand dollars
I NEED HELP FINDING:
b) Determine how many units should be produced for a profit of at least 40 thousand.
more than (thousands of) units
less than (thousands of) units
THANK YOU

Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
11 thousand units is correct, but 345 thousand dollars is not.

P(x)=-x^2+22x-18

P(11)=-(11)^2+22(11)-18 ... everywhere you see an 'x', replace it with 11

P(11)=-121+242-18

P(11)=103

So the correct max profit is 103 thousand dollars

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We want to solve P(x) >= 40

If we graph P(x)=-x^2+22x-18 (in green) and the horizontal line y = 40 (in blue), we get this

using the graphing calculator intersect feature, or the quadratic formula, we see that the solutions to -x^2+22x-18 = 40 are x = 3.062746067, x = 18.93725393. They are rough approximations

Round up to the nearest unit to get x = 3 or x = 19

So you need to produce more than 3 thousand units, but less than 19 thousand units to have a profit of at least 40 thousand.

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!

where:

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Complete the square

Take the square root of both sides

and

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More than 3,063 units and less than 18,937
units should be produced
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check my math, too

SOLUTION: The profit function for a computer company is given by P(x)=&#8722;x^2+22x&#8722;18 where x is the number of units produced (in thousands) and the profit is in thousand of dollars.

SOLUTION: The profit function for a computer company is given by P(x)=−x^2+22x−18 where x is the number of units produced (in thousands) and the profit is in thousand of dollars.