A-Electronics sells about 2000 of its new sim chips per month at a price of $35/chip. The production cost are $25/chip. The current policy is to replace any chips that fail within the first six months of installation. The dealer doing the replacement also gets $10 to cover the labour cost for the replacement. The competition has recently increased its guarantee period from 6 to 9 months. A-Electronics is now under pressure to follow suit or even go to a 12-months guarantee period. The engineering department has collected extensive data on replacements of chips, both under guarantee and after the guarantee period. They show the following picture, where time refers to the number of months after the initial installation of the chip(a) Management would like to know the increase in annual costs of extending the guarantee period from six months to 9, 12, 15, or 18 months. You need to find a functional relationship between the time and the number of replacements. What approximations, assumptions or boundary judgements do you make? (b) By how much would monthly sales have to increase to recover the increase in guarantee costs?