A Los Angeles firm uses a single input to produce a recreational commodity according to a production function f(x) = 4x, where x is the number of units of input. The commodity sells for $100 per unit. The

input costs $50 per unit.

1. Write down a function that states the firm's profit as a function of the amount of input.
2. What is the profit-maximizing amount of input?
3. What is the profit-maximizing amount of output?
4. How much profit does it make when it maximizes profits?
5. Suppose that the firm is taxed $20 per unit of its output and the price of its input is subsidized by $10. What is its new input level?
6. What is its new output level?
7. How much profit does it make now?
8. Suppose that instead of these taxes and subsidies, the firm is taxed at 50% of its profits. Write down its after-tax profits as a function of the amount of input.
9. What is the profit maximizing amount of output?
10. How much profit does it make after taxes?

I need help with 3,4,6,7, and 10