Problem 5-6 A real estate agent is considering changing her cell phone plan. The

Question

Problem 5-6 A real estate agent is considering changing her cell phone plan. There are three plans to choose from, all o which involve a monthly service charge of $20. Plan A has a cost of $.38 a minute for daytime calls and $.17 a minute for evening calls. Plan B has a charge of $.47 a minute for daytime calls and $.14 a minute for evening calls. Plan C has a flat rate of $75 with 275 minutes of calls allowed per month and a charge of $.36 per minute beyond that, day or evening. a. Determine the total charge under each plan for this case: 120 minutes of day calls and 40 minutes of evening calls in a month. (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.) Cost for Plan A Cost for Plan B Cost for Plan C c. If the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal? (Round each answer to the nearest whole number.include the indifference point itself in each answer.) minutes Plan A is optimal from zero to onward. minutes. Plan C is optimal from d. Suppose that the agent expects both daytime and evening calls. At what point (ie, percentage of total call minutes used for daytime calls) would she be indifferent between plans A and B? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places. Omit the "%" sign in your response.) Point percent daytime minutes

Explanation / Answer

a. Cost for plan A = monthly service charge + day time call charge + night time call charge = $20+ 120 minutes*$0.38 + 40 minutes*$0.17 = 20+45.60+6.8 = $72.40

Cost for Plan B = 20+ 120*0.47 + 40*0.14 = 20+56.40+5.60 = $82.00

Cost for Plan C =20+75 = $95

c. If the agent uses the service only for daytime calls then let the no. of call minutes for which plan A will be optimal be “x”. Thus cost of A = 20+0.38x. Cost of C = 20+75 = 95.

Thus 20+0.38x<95

Or 0.38x<75

Or x<75/0.38 = 197.37 minutes

Thus the range for plan A is zero to 197 minutes.

Plan C is optimal from 197 minutes onward.

d. Let the % of total call minutes used for daytime calls be x. Thus % of minutes for evening calls = 100-x. Cost in case of Plan A = 20+(0.38*x/100)+(0.17*(100-x)/100)

=20+(0.21x+17)/100

Cost in case of Plan B = 20+(0.47*x/100)+(0.14*(100-x)/100)

= 20+(0.33x+14)/100

At the point of indifference both the costs will be the same. So 20+(0.21x+17)/100 = 20+(0.33x+14)/100

Or 0.21x+17 = 0.33x+14

Or 0.12x = 3

Or x = 3/0.12 = 25%

Thus the answer is 25.00%

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