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 $.42 a minute for daytime calls and $.17 a minute for evening calls. Plan B has a charge of $.52 a minute for daytime calls and $.15 a minute for evening calls. Plan C has a flat rate of $80 with 275 minutes of calls allowed per month and a charge of $.38 per minute beyond that, day or evening.a. Determine the total charge under each plan for this case: 150 minutes of day calls and 70 minutes of evening calls in a month. (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)b. 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.)c. 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?

Answer 1

Answer:

req 1)

Plan A

0.42 x 150 + 0.17 x 70 = 74.9

Plan B

0.52 x 150 + 0.15 x 70 = 88.5

Plan C  $80

req 2)

from 0 to 190 minutes Plan A

from 191 and beyond Plan C

req 3)

the proportion should be 1/6 daycalls and 5/6 evenings

Explanation:

150 day calls

70 minutes evening calls

Plan A

0.42 x 150 + 0.17 x 70 = 74.9

Plan B

0.52 x 150 + 0.15 x 70 = 88.5

Plan C  $80

2) A will be preferable to B as it has the lower cost

now at some point C will be better as the cost is a flat rate

80 dollars / 0.42 per minute = 190.47

3) 0.42X + 0.17Y = 0.52X + 0.15Y

a minute of daycall is 10 cent higher in plan B

while a minute of evening call is 2 cent lower

thus, to balance there was to be 5 times more evening call than day times:

1:5 1 + 5 = 6

the proportion should be 1/6 daycalls and 5/6 evenings