Question

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)?

Answer 1

1, 2, 3, 4, or 6 years?

Answer 2

Hmm... http://www.openstudy.com/study#/updates/52654419e4b040e33d2c9a43

Answer 3

theres no answer on that ://

Answer 4

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

Answer 5

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 :)

Answer 6

thank you :D

Answer 7

No problem :)