Suppose a shop needs to have an ice shaver machine over the next five years period. A new ice shaver machine cost $1,000. The machine deteriorates with age and requires to trade in for a new one every three year of usage. The trade in value and the maintaining cost are given in below table. Age of machine (year) Maintenance cost ($) Trade in value (5) 1 60 800 2 80 600 3 120 500 (a) Use dynamic programming to find the optimal purchasing policies or strategies, so as to minimize the total cost over a period of 5 years and leaves the shop with a new ice shaver machine at the end of the period. [23 marks] (b) Based on the optimal purchasing policy obtained in (a), how many percent of the shop's saving should be spent for the ice shaver machine, if the shop has $10.240 in saving. [2 marks]