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An entrepreneur estimates his total profit (total revenue minus total cost) for his proposed company as p(x) = x3 − 4x2 + 5x − 20, where p is in hundreds of dollars and x is number of years the company has been in business. Identify the year (x) the entrepreneur will break even.

Ayear 1
Byear 2
Cyear 3
Dyear 4

Verified Answer :

carlosego

break even means that the total income is equal to the total cost.

Therefore, we can equal the total gain to zero.

We have then:


\(p (x) = x ^ 3 - 4x^2 + 5x - 20\)

Equaling zero we have:

\(x ^ 3 - 4x^2 + 5x - 20 = 0\)

Rewriting the polynomial we have:


\((x-4) (x ^ 2 + 5) = 0\)

We observe that the polynomial only has a real solution.

Therefore we have:

\(x-4 = 0x = 4\)

Answer:

the year (x) the entrepreneur will break even is:

D. year 4

Lanuel

The number of year (x) that it would take for this entrepreneur to break even is equal to: D. year 4.

How to calculate the year (x) this entrepreneur will break even?

In Economics, breaking even implies that the total revenue of an entrepreneur would be equal to the total cost. Thus, we would equate the total profit to zero as follows:

P(x) = x³ - 4x² + 5x - 20

Equating to zero, we have:

x³ - 4x² + 5x - 20 = 0

Simplifying the polynomial, we have:

(x - 4)(x² + 5) = 0

Note: The polynomial above only has a real solution.

x - 4 = 0

x = 4 years.

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