Question

A real estate agent is considering changing her land line 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 $.41 a minute for daytime calls and $.16 a minute for evening calls. Plan B has a charge of $.51 a minute for daytime calls and $.15 a minute for evening calls. Plan C has a flat rate of $80 with 300 minutes of calls allowed per month and a charge of $.38 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 $
b. 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.)
c. 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.)

Answer 1

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.

• Cost for Plan A = ($0.41 x 120) + ($0.16 x 40) + $20 = $ 75.60
• Cost for Plan B = ($0.51 x 120) + ($0.15 x 40) + $20 = $ 87.20
• Cost for Plan C = $80 + $20 = $100

b. If the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal?

• If the agent will use the service only for daytime calls, Plan A is better if the agent uses 195 minutes maximum. If the agent expects to use 196 or more minutes, then Plan C is better.

c. 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?

• Plan A charges 10¢ less per daytime minute, while plan B charges 1¢ less for evening minutes, that means that the proportion of daytime calls should be 1/11, while the proportion of evening calls should be 10/11.