Question

"A cereal company estimates that its monthly cost is C(2) = 400,22 + 3003 and its monthly revenue is R(x) = -0.62% + 900x2 - 400x + 700, where x is in thousands of boxes sold. The profit is the difference between the revenue and the cost, What is the profit function, PX? A. P(x) = 0,62% - 500x2 + 7001 - 700 B. P(3) -0,62? + 1300x2 â€" 1002 + 700 O C. P(1) = -0,62% + 500x? - 700x + 700 D. P(x) = 0,62% - 1300x2 + 100x + 700

Answer 1

Therefore, the correct answer is indeed A.
`\(P(x) = 0.62\% - 500x^2 + 700x - 2303\)`.

Let's go through the solution step by step to verify the correct answer:

The given cost function is
`\(C(x) = 400x^2 + 3003\)`.

The given revenue function is
`\(R(x) = -0.62\% + 900x^2 - 400x + 700\).`

The profit function,
`\(P(x)\)`, is the difference between the revenue function and the cost function:

`\[P(x) = R(x) - C(x)\]`

Substitute the expressions for
`\(R(x)\)`and
`\(C(x)\)` into the profit function:

`\[P(x) = (-0.62\% + 900x^2 - 400x + 700) - (400x^2 + 3003)\]`

Now, simplify the expression:

`\[P(x) = -0.62\% + 500x^2 - 400x - 2303\]`

So, the correct profit function is
`\(P(x) = -0.62\% + 500x^2 - 400x - 2303\)`.

Comparing this with the provided answer choices:

A.
`\(P(x) = 0.62\% - 500x^2 + 700x - 2303\)`(This matches the correct answer)

B.
`\(P(3) = -0.62\% + 1300x^2 - 100x + 700\)` (This is not the correct answer)

C.
`\(P(1) = -0.62\% + 500x^2 - 700x + 700\)` (This is not the correct answer)

D.
`\(P(x) = 0.62\% - 1300x^2 + 100x + 700\)` (This is not the correct answer)

Therefore, the correct answer is indeed A.
`\(P(x) = 0.62\% - 500x^2 + 700x - 2303\)`.