Question

A real estate agent is considering changing her cell phone plan; there are three to chose from - all involve a monthly fee of $20.75

Plan A charges $0.35 per minute for daytime calls and $0.24 per minute for evening calls.

Plan B charges $0.58 per minute for daytime calls and $0.16 per minute for evening calls.

Plan C has a flat rate of $39 with up to 200 minutes of calls included per month and a charge of $0.33 per minute beyond that, day or evening.

If the agent will use the service for daytime calls only, how many minutes per month should she stay below so that Plan A is the least cost alternative?

Answer 1

If we compare A & B. For any nubers of calls cost of Plan A will be less than Plan B. Because monthly fee is same in both the planes while variable rate per minute is less in plan A. Hence A will always be less costly as compared to Plan B.

So we have to compare plan A and plan C only.Monthly fee is same in both the plans.

Plan C has two ranges

• upto 200 minutes
• more than 200 minutes

So we will calculate two break even for both the ranges.

A) UPTO 200 MINUTES

Cost of Plan C ( maximum nd fixed ) = 39$

So cost of plan A upto 35$ will be considered as break even.

Max minutes = cost of plan C / Rate of plan A = 39$ / 0.35 = 111.42

It means cost upto 111 minutes will be less in plan A as compared to Plan C.

B) ABOVE 200 MINUTES

Cost of Plan C = 39$ + 0,33 ABOVE 200 MINUTES.

Cost of Plan A = 0.35 per minute

Break even = Difference in fixed cost / difference in variable cost

= (39 - 0 ) / (0.35-0.33) = 1950 minutes.

Hence Above 200 minutes , cost upto 1950 Minutes will be less costly in Plan A.

CONCLUSION

Range	Which plan is less costly
Upto 111 minutes	Plan A
Above 111 minutes but less than 200 minutes	Plan C
Above 200 but less than 1950 minutes	Plan A
Above 1950 minutes	Plan C