Task 4 - Optimisation and Production (Maximum 10 Marks) Learning Outcome KU1) demonstrate mathematical literacy by consistently using correct Mathematical notation, terminology, conventions, and relevant diagrams and graphs; Two firms' short-run production functions are given by:- BL-8 Q. = 30012 - NL and Q= where L denotes the number of workers and N is the last non-zero digit of your Student Identity Number. The marginal product of labour MP, is given by the derivative of production with respect to labour. The average product of labour AP, is taken to be the total output divided by the labour. It measures the average output per worker and it is sometimes called labour productivity. Find the size of the workforce that maximises the average product of labour in both situations and verify that at this value of L we have MPL = AP for both models. Compare the two models for the two firms sketching the graphs of MP, and AP, for both firms and describing the relationship between MP, and AP, in the different phases of the production for the two models. KU2) evaluate the strengths and weaknesses of alternative models and consequently of any conclusions drawn; SS4) solve a range business-related problems either deterministically or probabilistically as appropriate; SS5) choose and apply appropriate techniques in algebra, and calculus in finding a solution to a problem: KE6) use a range of IT packages, including calculators, spreadsheets, word processors and skills in the analysis and solution of business problems; KE7) communicate their work effectively, presenting their solutions using an appropriate medium