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 longdistance 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 a minutes of local calls and b minutes of long-distance calls.

Questions:

(a) Using a max objective function write expressions for the total cost of each Plan in terms of a and b. If a = 1100, and b = 100, find the cost of each Plan.

(b) ) For a+b 1200, find the values for a and b that would make Plan 1 better (i.e. cheaper) than Plan 2. Based on this solution, show the region on the graph below where Plan 1 is better than Plan 2.

200 b 0 200 400 600 800 1000 1200 a