A firm in a perfectly competitive industry receives priceAfor each unit of its output. It payswto its employees for each hour worked,h. The firm pays a fixed cost ofB. The quantity produced, output, is determined by the functionq(h).

(7) (i) Write down the firm's revenue, costs, and profit functions. Clearly label each.

Now suppose that:

q(h)=ah

where 'a' is a constant positive value.

(7) (ii) How many hours worked would maximize firm profits?

(7) (iii) Prove that your result in part (ii) is a maximum.