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Natasha is considering two mobile phone plans. Plan 1 would cost $27 and would give her 800 minutes of free local calls. Extra local calls, and any long distance calls would cost $0.36 per minute. Plan 2 would cost $45, and there would be 1200 minutes of local or long-distance minutes; over this limit calls would cost $0.36 per minute. Suppose that she wishes to make aminutes of local calls and b minutes of long-distance calls.
(a) Using a max function write expressions for the total cost of each Plan in terms of aand b.
(b) If a= 1100, and b= 100, find the cost of each Plan.
(c) For a+b≤1200, find the values for aand bthat would make Plan 1 better (i.e. cheaper) than Plan 2.
(d) Based on the solution for (c), show the region on the graph below where Plan 1 is better than Plan 2.0
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