SOLUTION: HI! Im having troubles with quadratic equations! i was hoping you could show me all the steps? My question is: The Wheely Fast Co. makes custom skateboards for professional rid

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: HI! Im having troubles with quadratic equations! i was hoping you could show me all the steps? My question is: The Wheely Fast Co. makes custom skateboards for professional rid      Log On


   

Question 963939: HI! Im having troubles with quadratic equations! i was hoping you could show me all the steps? My question is:
The Wheely Fast Co. makes custom skateboards for professional riders. they model their profit with the relation P= -2b^2 + 14b - 20, where b is the number of skate boards they produce (in thousands) and P is the company's profit in hundred thousands of dollars.
How many skateboards foe Wheely Fast need to produce to maximize profit?
Thank you so much!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

P=+-2b%5E2+%2B+14b+-20
set P=0 and find b
0=+-2b%5E2+%2B+14b+-20..........factor out -2
0=+-2%28b%5E2+-7b+%2B10%29....factor -1 out
0=+-2%28b%5E2+-+7b+%2B10%29......write -7b as -2b-5b
0=+-2%28b%5E2+-+2b-5b+%2B10%29...group
0=+-2%28%28b%5E2+-+2b%29-%285b+-10%29%29
0=+-2%28b%28b+-+2%29-5%28b+-2%29%29
0=+-2%28%28b-5%29%28b+-2%29%29
solutions:
b=5 and b=2=> since in thousands, company need to produce 5000 or 2000 skateboards to break even
maximum profit occurs at b=%285%2B2%29%2F2=7%2F2=3.5=> in thousands 3500
so, foe Wheely Fast need to produce ............substitute b=3.5
P=+-2%28%283.5-5%29%283.5+-2%29%29
P=+-2%28-1.5%29%281.5%29
P=+-2%28-1.5%29%281.5%29
P=+-2%28-2.25%29
P=+4.5=> in hundred thousands of dollars will be P=+450000