Given that the demand function for an item is = 20 - 8 , where is price and Q quantity.

a) Express the income function as a function of . is quantity. (In English, the revenue function is often called TR = Total Revenue) The company's fixed costs are 4 and the variable costs are given by the function 7 + 15 per unit produced.

b) Write down the expression for the cost function. (In English, the cost function is often called TC = Total Cost) = ()

c) Use the answers from a and b to formulate the expression for the company's profit function (often denoted by )

d) Find the production volumes () where the company balances. e) Find an expression for the marginal income (MR) and an expression for the marginal cost (MC) f) For which production volume () does the company maximize profits? Justify the answer.