Question

The profit of a company is modeled by the equation p(x) = 60x − 2x2 − 2, where p the profit is in thousands of dollars and x is the number of units sold in hundreds. How many units must the company sell to make the maximum profit?

1,000

1,500

2,000

2,500

Answer 1

p(x)=60x-2x^2-2

Answer 2

Well, in order to find the maximum profit, we would have to find, the functions maximum value.
And to do that, we have to derivate the function:
\[p(x)=60x-2x^2-2\]
and derivating it:
\[p'(x)=60-4x\]
Then, a maximum is determined when the derivative is zero:
\[60-4x=0\]
\[x=15\]

Answer 3

so what do I do with the 15?

Answer 4

evaluate it in the original function P(x)

Answer 5

plug in the 15s for x?

Answer 6

yes

Answer 7

60(15)-2(15)^2-2

Answer 8

I didnt get nowhere near the answers

Answer 9

what did you get?

Answer 10

448

Answer 11

yes, it's correct, but I gave you the answer, re-read the question.

Answer 12

so its 1500

Answer 13

correct