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.

     

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	$ ________

       

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

Answer 1

a.

Cost of Plan A = 20 + 0.38*120 +0.17*40 = $72.40

Cost of Plan B = 20 + 0.47*120 + 0.14*40 = $82.00

Cost of Plan C = 20 + 75 = $95

c.

The range of calls which plan A is the most economical = (75 + 20 – 20) / 0.38 = 197 calls

d.

Let x be the percentage of total call minutes used for daytime calls, at which she would be indifferent between plans A and B. which means at that percentage, total cost of plan A and B are equal.

Cost of plan A = 0.38x + (1-x)*0.17

Cost of plan B = 0.47x + (1-x)*0.14

0.38x + (1-x)*0.17 = 0.38x + (1-x)*0.17

=> 0.21x + 0.17 = 0.33x + 0.14

=>(0.33 – 0.21)x = 0.17 - 0.14

=>0.12x = 0.03

=> x = 0.03/0.12 = 0.25 = 25% for days calls