Help solve this problem

[avinash77]

Suppose that you can sell as much of a product (in integer units) as you like at $63 per unit. Your marginal cost (MC) for producing the qth unit is given by:

MC=6qMC=6q
This means that each unit costs more to produce than the previous one (e.g., the first unit costs 6*1, the second unit (by itself) costs 6*2, etc.).

If fixed costs are $90, what is the profit at the optimal output level?

Please specify your answer as an integer.

[Algaeconomics]

I'm not sure but here is my take on it

profit function = 63Q- 3Q^2 - 90

Maximizing we get

63 - 6Q = 0

Q= 10.5

So the maximum profit is 240.75 when Q= 10.5
But we are allowed to use only integer numbers for Q. So we will look for the integers near 10.5 which are 10 and 11

Now at Q=10 the profit is 630-(390)= 240
At Q=11 the profit is 693-(453) = 240

So the profit levels for both Q=10 and Q=11 are the same, he should be indifferent between producing either.