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 $.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 $.40 per minute beyond that, day or eveninga. Determine the total charge under each plan for this case: 120 minutes of day calls and 40 minutes of evening calls in a month. (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" 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

Answer:

A would be the best plan for the given use of 120 minutes durng daytiem and 40 minutes evening call.

B)

for only daytieme calls as Plan A has a lower rate in dayime than B it wil lbe always preferable over it. Now as point C has a flat rate plant A will be a better option below it:

$80 / 0.45 = 178 minutes

After this point plant A will surpass the 80 dollars flat rate charged by C therefore, be more expensive

from 0 to 178 Plan A

from 178 and above Plan C

Explanation:

               Plan A  Plan B Plan C*

daytime  0.45        0.55    0.40

evening  0.20        0.12      0.40

*Plan C cost per minute start after 200 minutes.

at 120 daytime and 40 evening call:

A) 120 x 0.45 + 40 x 0.20 =     62.00  

B) 120 x 0.55 + 40 x  0.12 =      70.80  

C) $200

Answer 2

Cost for Plan A , B and C are $76.1 , $86.8 and $95

Cost for Plan A = $20 + $0.37(130) + $0.16(50)

Cost for Plan A = $20 + $48.10 + $8

Cost for Plan A = $76.1

Cost for Plan B = $20 + $0.46(130) + $0.14(50)

Cost for Plan B = $20 + $59.80 + $7

Cost for Plan B = $86.8

Cost for Plan C = $20 + $75

Cost for Plan C = $95

                                                                                                                     

Plan A is optimal from zero to = $20 + $0.37D

Plan A is optimal from zero to = $20 + $0.37(75)

Plan A is optimal from zero to = $95

                                                                                                                     

Indifferent between plans A and B (D) = $75 / $0.37

Indifferent between plans A and B (D) = 202.70 minutes

                                                                                                                       

Plan A is best for periods of zero to 203 minutes. Plan C is best when you have 203 minutes or more.

A =  $20 + $0.37D + $0.16E ........... Eq1

B = $20 + $0.46D + $0.14E ............ Eq2

From EQ1 and EQ2

0.37D + 0.16E = 0.46D + 0.14E

0.02E = 0.09D

E = ($0.09/$0.02)D

E = 4.5D

So, D = 100 minutes

E = 450 minutes

Percent of Daytime Minutes = [100 / (450 + 100)]

Percent of Daytime Minutes = 100/550

Percent of Daytime Minutes = 18.18%

Plan A is best for periods of zero to 203 minutes. Plan C is best when you have 203 minutes or above.

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