This is the full question, in "a" you should write a function that states the firm's profit as a function of the amount input. I am guessing it should be done in a general sense? Like p1x1 + p2x2 = m But ofcourse now instead use a general production function.

A company uses a single input to produce a commodity according to a production function , where x is the number of units of input. The commodity sells for $20 per unit. The input costs $5 per unit. Write down a function that states the firm's profit as a function of the amount of input. What is the profit-maximizing amount of input? What is the profit-maximizing amount of output?How much profits does the firm make when it maximizes profits? Suppose that the firm is taxed $10 per unit of its output and the price of its input is subsidized by $2. (Assume that the price of output is unchanged, i.e. still $20). What is its new input level? What is its new output level? How much profit does it make now? Suppose that instead of these taxes and subsidies, the form is taxed at 50% of its profits. Write down its after-tax profits as a function of the amount of input. What is the profit-maximizing amount of output? How much profit does it make after taxes? . A company uses a single input to produce a commodity according to a production function , where x is the number of units of input. The commodity sells for $20 per unit. The input costs $5 per unit. Write down a function that states the firm's profit as a function of the amount of input. What is the profit-maximizing amount of input? What is the profit-maximizing amount of output?How much profits does the firm make when it maximizes profits? Suppose that the firm is taxed $10 per unit of its output and the price of its input is subsidized by $2. (Assume that the price of output is unchanged, i.e. still $20). What is its new input level? What is its new output level? How much profit does it make now? Suppose that instead of these taxes and subsidies, the form is taxed at 50% of its profits. Write down its after-tax profits as a function of the amount of input. What is the profit-maximizing amount of output? How much profit does it make after taxes