Chapter 5, Problem 6P

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 $.45 a minute for daytime calls and $.20 a minute for evening calls. Plan B has a charge of $.55 a minute for daytime calls and $.15 a minute for evening calls. Plan C has a flat rate of $80 with 200 minutes of calls allowed per month and a charge of $.40 per minute beyond that, day or evening.

a. Determine that total charge under each plan for this case: 120 minutes of day calls and 40 minutes of evening calls in a month.

b. Prepare a graph that shows total monthly cost for each plan versus daytime call minutes.

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

d. Suppose that the agent expects both daytime and evening calls. At what point (i.e., percentage of call minutes for daytime calls) would she be indifferent between plans A and B?

Summary Introduction

To determine: The total charge of each plan for 120 minutes of day calls and 40 minutes of evening calls.

Introduction: Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Answer to Problem 6P

Hence, the total cost of Plan A is $82, Plan B is $92, and Plan C is $100.

Explanation of Solution

Given information:

A real estate is considered changing her cell phone plan which incurs a monthly service charge of $20. There are three plans available.

Plan A: $0.45 per minute for a day calls and $0.20 per minute for evening calls.

Plan B: $0.55 per minute for a day calls and $0.15 per minute for evening calls.

Plan C: $80 for allowed 200 calls per month and $0.40 per minutes beyond that irrespective of day or evening

Calculate the total cost for Plan A:

It is calculated by adding the monthly service charge, the multiple of cost per minute of day calls and total minutes given for day calls, and the multiple of cost per minute of evening calls and total minutes given for evening calls.

$\begin{array}{lll}\begin{array}{l}\text{Total}\text{cost}\\ \text{for Plan A}\end{array}\}\hfill & =\hfill & \text{Monthly charge +}\left(\begin{array}{l}\text{Cost per minute for day calls }\times \\ \text{Total day calls minutes}\end{array}\right)+\left(\begin{array}{l}\text{Cost per minute for evening calls }\times \\ \text{Total evening calls minutes}\end{array}\right)\hfill \\ \hfill & =\hfill & \$20+(\$0.45\times 120)+(\$0.20\times 40)\hfill \\ \hfill & =\hfill & \$20+\$54+\$8\hfill \\ \hfill & =\hfill & \$82\hfill \end{array}$

Hence, the total cost for Plan A is $82.

Calculate the total cost for Plan B:

It is calculated by adding the monthly service charge, the multiple of cost per minute of day calls and total minutes given for day calls, and the multiple of cost per minute of evening calls and total minutes given for evening calls.

$\begin{array}{lll}\begin{array}{l}\text{Total}\text{cost}\\ \text{for Plan B}\end{array}\}\hfill & =\hfill & \text{Monthly charge +}\left(\begin{array}{l}\text{Cost per minute for day calls }\times \\ \text{Total day calls minutes}\end{array}\right)+\left(\begin{array}{l}\text{Cost per minute for evening calls }\times \\ \text{Total evening calls minutes}\end{array}\right)\hfill \\ \hfill & =\hfill & \$20+(\$0.55\times 120)+(\$0.15\times 40)\hfill \\ \hfill & =\hfill & \$20+\$66+\$6\hfill \\ \hfill & =\hfill & \$92\hfill \end{array}$

Hence, the total cost for Plan B is $92.

Calculate the total cost for Plan C:

It is calculated by adding monthly service charge, call cost for the allowed 200 minutes, and the multiple of call minutes beyond 200 and the cost per minutes. The total call minutes is 160 (120+40). As it does not exceed 200 minutes, there would 0 remaining minutes.

$\begin{array}{lll}\text{Total cost for plan C}\hfill & =\hfill & \text{Monthly charge +}\left(\begin{array}{l}\text{Cost per }\\ \text{200 minutes}\end{array}\right)+\left(\begin{array}{l}\text{Cost per minute}\times \\ \text{Total minutes beyond 200}\end{array}\right)\hfill \\ \hfill & =\hfill & \$20+\$80+(\$0.40\times 0)\hfill \\ \hfill & =\hfill & \$20+\$80+\$0\hfill \\ \hfill & =\hfill & \$100\hfill \end{array}$

Hence, the total cost for Plan C is $100.

Summary Introduction

To prepare: A graph for monthly charge for each plan versus day time minutes.

Introduction: Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Answer to Problem 6P

The graph has been drawn.

Explanation of Solution

Given information:

A real estate is considered changing her cellphone plan which incurs a monthly service charge of $20. There are three plans available.

Plan A: $0.45 per minute for a day calls and $0.20 per minute for evening calls.

Plan B: $0.55 per minute for a day calls and $0.15 per minute for evening calls.

Plan C: $80 for allowed 200 calls per month and $0.40 per minutes beyond that irrespective of day or evening

Prepare a graph of monthly charge for each plan versus day time minutes:

Summary Introduction

To determine: The optimal call minutes for each plan if the agent would use only day calls.

Introduction: Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Answer to Problem 6P

Plan A would be optimal when the day minutes is less than 177.78 minutes.

Explanation of Solution

Given information:

A real estate is considered changing her cellphone plan which incurs a monthly service charge of $20. There are three plans available.

Plan A: $0.45 per minute for a day calls and $0.20 per minute for evening calls.

Plan B: $0.55 per minute for a day calls and $0.15 per minute for evening calls.

Plan C: $80 for allowed 200 calls per month and $0.40 per minutes beyond that irrespective of day or evening

Determine the optimal call minutes for each plan if the agent would use only day calls:

$\begin{array}{lll}\text{Plan}\text{A}\hfill & =\hfill & \$20+\$0.45D\hfill \\ \text{Plan B}\hfill & =\hfill & \$20+\$0.55D\hfill \end{array}$

D refers to day time calls

The volume of Plan B is more than Plan A. Hence, it should be omitted, as it would obvious have high cost.

Calculate the total cost for Plan C:

It is calculated by adding monthly service charge, call cost for the allowed 200 minutes, and the multiple of call minutes beyond 200 and the cost per minutes. The total call minutes is 160 (120+40). As it does not exceed 200 minutes, there would 0 remaining minutes.

$\begin{array}{l}\begin{array}{lll}\text{Total cost for plan C}\hfill & =\hfill & \text{Monthly charge +}\left(\begin{array}{l}\text{Cost for allowed }\\ \text{200 minutes}\end{array}\right)+\left(\begin{array}{l}\text{Cost per minutes}\times \\ \text{Total minutes beyond 200}\end{array}\right)\hfill \\ \hfill & =\hfill & \$20+\$80+(\$0.40\times 0)\hfill \\ \hfill & =\hfill & \$20+\$80+\$0\hfill \\ \hfill & =\hfill & \$100\hfill \end{array}\\ \end{array}$

Hence, the total cost for Plan C is $100.

Determined the value of D in the equation of Plan A by comparing the equation with the total cost of Plan C:

The equation of Plan A (considering the day calls) should be compared with the total cost of Plan C.

$\begin{array}{lll}\$20+\$0.45D\hfill & =\hfill & \$100\hfill \\ \$0.45D\hfill & =\hfill & \$100-\$20\hfill \\ D\hfill & =\hfill & \frac{\$80}{\$0.45}\hfill \\ \hfill & =\hfill & 177.78\hfill \end{array}$

Hence, the day call minutes are 177.78 minutes.

Conclusion: Plan A would be optimal when the day call minutes are less than 177.78 minutes and Plan C would be optional when it exceeds up to 200 minutes.

Summary Introduction

To determine: The percentage of call minutes would be indifferent between Plan A and Plan B if the agent would both day calls and evening calls.

Introduction: Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Answer to Problem 6P

The percentage of call minutes is 33.33%.

Explanation of Solution

Given information:

A real estate is considered changing her cellphone plan which incurs a monthly service charge of $20. There are three plans available.

Plan A: $0.45 per minute for a day calls and $0.20 per minute for evening calls.

Plan B: $0.55 per minute for a day calls and $0.15 per minute for evening calls.

Plan C: $80 for allowed 200 calls per month and $0.40 per minutes beyond that irrespective of day or evening

Determine the percentage of call minutes would be indifferent between Plan A and Plan B if the agent would both day calls and evening calls:

$\begin{array}{lll}\text{Plan}\text{A}\hfill & =\hfill & \$20+\$0.45D+\$0.20E\hfill \\ \text{Plan}\text{B}\hfill & =\hfill & \$20+\$0.55D+\$0.15E\hfill \end{array}$

D refers to day time calls

E refers to evening calls

Compare the equations to solve D:

The equation of Plan A and Plan B considering both day and evening calls should be compared to determine the value of D.

$\begin{array}{lll}\$20+\$0.45D+\$0.20E\hfill & =\hfill & \$20+\$0.55D+\$0.15E\hfill \\ \$0.45D+\$0.20E\hfill & =\hfill & \$0.55D+\$0.15E\hfill \\ \$0.45D-\$0.55D\hfill & =\hfill & \$0.15E-\$0.20E\hfill \\ -\$0.10D\hfill & =\hfill & -\$0.05E\hfill \\ D\hfill & =\hfill & \frac{-\$0.05}{-\$0.10}E\hfill \\ \hfill & =\hfill & 0.5E\hfill \end{array}$

It should that day calls are half of the evening calls.

For example: If E=100 minutes,

$\begin{array}{lll}D\hfill & =\hfill & 0.5E\hfill \\ \hfill & =\hfill & 0.5E\times \hfill \\ \hfill & =\hfill & 50\text{minutes}\hfill \end{array}$

It states the following equations:

$\begin{array}{lll}D\hfill & =\hfill & \left(\frac{50}{100+50}\right)\hfill \\ \hfill & =\hfill & \frac{50}{150}\hfill \\ \hfill & =\hfill & 0.0333\times 100\hfill \\ \hfill & =\hfill & 33.33\%\hfill \end{array}$

Hence, at 33.33% of total call time, the agent would be indifferent between the plans A and B.