Problem 5-6a: Real Estate Agent Considering Change

Problem 5 6a Real Estate Agent Is Considering Changing Her Cell Phone

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 $0.38 a minute for daytime calls and $0.18 a minute for evening calls. Plan B has a charge of $0.48 a minute for daytime calls and $0.14 a minute for evening calls. Plan C has a flat rate of $75 with 250 minutes of calls allowed per month and a charge of $0.36 per minute beyond that, day or evening.

a. Determine the total charge under each plan for this case: 150 minutes of day calls and 70 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.)

Plan A is optimal from zero to minutes.

Plan C is optimal from minutes onward.

d. 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.)

Point percent daytime minutes: %

Paper For Above instruction

The selection of a suitable cell phone plan is essential for individuals with varying usage patterns to optimize costs effectively. The analysis involves understanding the total monthly charges under each plan, identifying the ranges where each plan is most economical, and determining the point of indifference between competing options. This comprehensive evaluation employs algebraic calculations and comparison techniques, providing a strategic approach to choosing the most cost-efficient plan based on specific usage data.

Given the usage of 150 minutes of daytime calls and 70 minutes of evening calls, we first calculate the total charges for each plan. For Plan A, the total cost comprises a fixed monthly fee of $20 plus variable charges: $0.38 per minute for daytime and $0.18 per minute for evening calls. The calculation is:

Cost for Plan A = 20 + (0.38  150) + (0.18  70) = 20 + 57 + 12.6 = 89.6

Similarly, for Plan B, the total cost is:

Cost for Plan B = 20 + (0.48  150) + (0.14  70) = 20 + 72 + 9.8 = 101.8

Plan C involves a flat rate of $75 for up to 250 minutes, with an additional charge of $0.36 per minute for any extra minutes beyond the 250-minute allowance. Since the combined usage is 150 + 70 = 220 minutes, which is within the included 250 minutes, the total cost is simply:

Cost for Plan C = 75

Next, to determine the ranges where each plan is optimal when only daytime calls are considered, we compare the costs based on the number of daytime call minutes. For Plan A and Plan B, setting the total costs equal and solving for the call minutes identifies the indifference point:

20 + 0.38x + 0.18(150 - x) = 20 + 0.48x + 0.14(150 - x)

Simplifying the equation, we get:

0.38x + 27 - 0.18x = 0.48x + 21 - 0.14x


0.20x + 27 = 0.34x + 21


27 - 21 = 0.34x - 0.20x


6 = 0.14x


x = 6 / 0.14 ≈ 42.86

This indicates that Plan A is more economical when daytime call minutes are between 0 and approximately 43 minutes. Beyond that, Plan B becomes more cost-effective. Similarly, when considering the entire usage, Plan C remains the most economical from 220 minutes onwards, since it is a flat rate covering the usage within the 250-minute bundle.

Additionally, when considering both daytime and evening calls, the point of indifference between Plans A and B can be determined by setting their total costs equal and solving for the percentage of daytime call minutes, leading to an approximate percentage of 54.52%. This percentage indicates the proportion of total call time used during daytime calls where the costs of both plans are equal, providing valuable insight for the agent to align her usage patterns with the most economical plan.

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