02.07.2022 - 05:02

# Suppose that the agent expects both daytime and evening calls. At what point (i.e., 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 pe

Question:

Suppose that the agent expects both daytime and evening calls. At what point (i.e., 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.)

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 $20. Plan A has a cost of$.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. Answers (1) • April 17, 2023 в 13:14 The agent would be indifferent between plans A and B when the cost of using each plan is the same. Let x be the percentage of total call minutes used for daytime calls. Then the cost of using plan A is:$20 + 0.38x(daytime minutes) + 0.17(1-x)(evening minutes) And the cost of using plan B is: \$20 + 0.47x(daytime minutes) + 0.14(1-x)(evening minutes) Setting these two expressions equal to each other and solving for x, we get: 20 + 0.38x + 0.17 - 0.17x = 20 + 0.47x + 0.14 - 0.14x 0.21x = 0.13 x = 0.619 or 61.9% Therefore, if the agent expects to use 61.9% or more of her total call minutes during the daytime, she should choose plan A. If she expects to use less than 61.9% of her total call minutes during the daytime, she should choose plan B.