Assume you are given the following production function: Q = 46L - L^2 + 11K - 0.

Assume you are given the following production function:

Q = 46L - L^2 + 11K - 0.5K^2

Since you are a price taker, you have to follow the market price for wages (w = 24), rental rate (r = 10), and the price for the produced good (p = 4).

1. Set up the profit function using the values above.
2. Assume we are in the short-run and capital (K) is fixed at 5 units. What is the optimal amount of labor?
3. Now, let's assume we are in the long-run, and thus no input is fixed. What is the marginal rate of technical substitution (MRTS)?