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) = x3 – 4x2 + 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

To determine the number of years when the company will breakeven, we use the equation given. At the breakeven point, the company has no profit and loses. So, we P(x) = 0. We calculate as follows:
P(x) = x3 – 4x2 + 3x – 12
0 = x^3 – 4x^2 + 3x – 12
x = 4 , 1.732i, -1.732i

Solving for x, we will have three value one real and 2 imaginary values. Since time cannot be negative and imaginary. The answer would be 4. After 4 years, the company will break even.