bry856
  • bry856
An entrepreneur estimates that the total profit (profit = total revenue minus total cost) from his proposed company will be given by the function P(x) = x^3 – 4x^2 + 3x – 12, where P is in hundreds of dollars and x is the number of years elapsed after the company starts operations. In how many years (x) will the company break even (no profit, no loss)?
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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bry856
  • bry856
1, 2, 3, 4, or 6 years?
anonymous
  • anonymous
Hmm... http://www.openstudy.com/study#/updates/52654419e4b040e33d2c9a43
bry856
  • bry856
theres no answer on that ://

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bry856
  • bry856
would it be 4 x can not be negative since it is time in years. so x-4 = 0 gives x=4; hence 4 years will bring in breakeven point
johnweldon1993
  • johnweldon1993
So we just need to find the roots of that expression \[\large P(x) = x^3 – 4x^2 + 3x – 12\] So we can factor this one easily by grouping \[\large 0 = (x^3 - 4x^2) + (3x - 12)\] Factor out an x^2 from the first...and factor out a 3 from the second \[\large x^2(x - 4) + 3(x - 4) = 0\] Combine the common factors and put the rest together \[\large (x-4)(x^2 + 3) = 0\] So solve that for x to make it equal 0 and as you just posted above...it is indeed 4 years :)
bry856
  • bry856
thank you :D
johnweldon1993
  • johnweldon1993
No problem :)

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