(a) When evaluating the predictive performance of a time series model, it is necessary to construct measures of accuracy. In your own words, discuss the relative advantage(s) and disadvantage(s) of any two measures of accuracy. Make sure you clearly define each measure with a suitable formula. Of these two measures, which one do you prefer, and why? (8 marks) (b) A profit-maximising manufacturer is deciding on its optimal product mix between two types of bookcase: standard bookcases (1) and deluxe bookcases (y). Each bookcase is made exclusively from wood, with no additional factor inputs. A standard bookcase is made using 30 kilograms of wood, while a deluxe bookcase is made from 40 kilograms of wood. The manufacturer has 8,000 kilograms of wood available for production. Standard bookcases generate a profit of 60 each, while deluxe bookcases generate a profit of 100 each. Given estimates about product demand from consumers, the number of standard bookcases should be at least double the number of deluxe bookcases. i. Formulate the manufacturer's decision as a linear programming problem, explaining the purpose of each equation. (5 marks) ii. Solve this linear programming problem graphically and by solving a pair of simultaneous equations, making sure you clearly indicate the set of feasible production bundles on your graph. (No graph paper required.) (7 marks) iii. Briefly discuss any recommendation(s) that you would make to this bookcase manufacturer so that it could increase profits beyond the amount you calculated in part