A firm producing lamps has fixed costs of 5000 per week. Each lamp costs 15 and it is sold for 35.

(i) Write the equations of the:

a) total cost function; b) total revenue function; c) profit function.

(ii) On the same diagram, graph the total cost function and the total revenue function. From the graph determine the break-even points. From the graph determine the profit when 300 lamps are sold. Confirm all the answers algebraically