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melomori [17]
2 years ago
9

The profit (in thousands of dollars) of a company is given by P(x) = -8x2 + 32x + 14.

Mathematics
1 answer:
andre [41]2 years ago
5 0

Answer:

C

Step-by-step explanation:

The profit (in thousands of dollars) of a company is given by the function:

\displaystyle P(x) = -8x^2+32x+14

And we want to find the maximum profit of the company.

Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex. Recall that the vertex of a quadratic is given by:

\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)

Find the <em>x-</em>coordinate of the vertex. In this case, <em>a</em> = -8, <em>b</em> = 32, and <em>c</em> = 14. Hence:

\displaystyle x=-\frac{(32)}{2(-8)}=\frac{32}{16}=2

To find the maximum profit, substitute this value back into the function. Hence:

\displaystyle P(2) = -8(2)^2+32(2) + 14 = 46

Therefore, the maximum profit of the company is 46 thousand dollars.

Our answer is C.

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