(10 marks) Betty is considering two mobile phone plans. Plan 1 would cost $18 per month and would give her 1000 minutes per month of free local calls. Extra local calls would cost $0.15 per minute, and any long-distance calls within the country would cost $0.30 per minute. Plan 2 would cost $75 per month, and would allow a month of unlimited calling within the country. Suppose that she wishes to make a minutes of local calls and b minutes of in-country long-distance calls per month. (a) Using a max function write an expression for the total cost of Plan 1 in terms of a and b . (b) Find the values for a and b that would make Plan 1 better (i.e. cheaper) than Plan 2. (c) Based on the solution for (b), show the region on the graph below where Plan 1 is better than Plan 2

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