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