Natasha is considering two mobile phone plans. Plan 1 would cost $30 and would give her 800 minutes of free local calls. Extra local calls, and any long- distance calls would cost $0.40 per minute. Plan 2 would cost $50, and there would be 1200 minutes of local or long-distance minutes; over this limit calls would cost $0.40 per minute. Suppose that she wishes to make a minutes of local calls and b minutes of long-distance calls. (a) Using the MAX function, write expressions for the total cost of each Plan in terms of a and b. (b) If a = 1100, and b = 100, find the cost of each Plan. (c) For a+b 1200, find the values for a and b that would make Plan 1 better (i.e. cheaper) than Plan 2. (d) Based on the solution for (c), show the region (see page 5) where Plan 1 is better than Plan 2.