The profit (in thousands of dollars) of a company is given by P(x) = -8x2 + 32x + 14. Find the maximum profit of the company.
O a. 40 thousand dollars
O b. 45 thousand dollars
O c. 46 thousand dollars

C

Step-by-step explanation:

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

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:

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

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

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

Our answer is C.

the correct answer is the second option