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 $.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.

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.)

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.)

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.

Explanation / Answer

Answer 1: Cost of Plan A = $72.40; Cost of Plan B = $82.00; Cost of Plan C = $90.00. (As explained below)

Plan A Cost:

Plan B Cost:

Plan C Cost:

Answer 2: Plan A is optimal from zero to 196 minutes. Plan C is optimal from 197 minutes onward. (As explained below)

If we compare the plans A and C, the fixed amount for Plan C is $75. If we allocate $75 to Plan A, then we can make 197 minutes of call. So, Plan A is optimum for less than 197 calls i.e. 196 calls. Plan C is optimum for 197 or more calls.

Answer 3: 33.34 percent daytime minutes. (As explained below)

If x and y be the number of calls made in daytime and evening, respectively. We need to find when the cost as per Plan A equals the cost as per plan B. So we have:

0.38x + 0.17y = 0.47x + 0.14y

9x = 3y

x/y = 1/3 = 0.33

So, the cost differential will be zero when the percentage of calls for daytime is 33.34.

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