A real estate agent is considering changing her cell phone plan. There are three

Question

A real estate agent is considering changing her cell phone plan. There are three plans to choose from, all of which involve a monthly service charge of $20. Plan A has a cost of $.45 a minute for daytime calls and $.20 a minute for evening calls. Plan B has a charge of $.55 a minute for daytime calls and $.15 a minute for evening calls. Plan C has a flat rate of $80 with 200 minutes of calls allowed per month and a charge of $.40 per minute beyond that, day or evening. Determine the total charge under each plan for this case: 120 minutes of day calls and 40 minutes of evening calls in a month. Prepare a graph that shows total monthly cost for each plan versus daytime call minutes. If the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal? Suppose that the agent expects both daytime and evening calls. At what point (i.e., percentage of call minutes for daytime calls) would she be indifferent between plans A and B?

Explanation / Answer

a) Total Charge under each Plan , 120 minutes of day call , 40 minutes of evining call

Total Cost for Plan A: $20 + $0.45(120) + $0.20(40) = $82
Total Cost for Plan B: $20 + $.55(120) + $.15(40) = $92
Total Cost for Plan C: $20 + $80 = $100

Thererfore she should choose plan A

C)

For Daytime plan A has always a better rate than plan B, Also plan C is better than plan A for when Time 200 minuts,

so there is point where Plan C turn to be better than plan A

that point is , 0.45 (T) =80

, so T < 178 , plan A will be optimal

so T 177 , plan C will be optimal,

d) Suppose Day start from 9:00 am to 6:00 pm ( total time is 9 hours, total minuts are 540 minutes

Cost of plan A ,if used 9 hour, is = 0.45 * 540 = $ 243

Cost of plan B ,if used 9 hour ,is = 0.55* 540 = $297

% of indifference is = ( ( $297 - $ 243) / $ 243 ) * 100 = 22.22%

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