A household uses at least 3000 minutes of long-distance telephone calls monthly and can choose to use the services of any of three companies: A, B and C. Company A charges a fixed monthly fee of $10 and 5 cents per minute for the first 1000 minutes and 4 cents per minute for all additional minutes. Company B’s monthly fee is $20 with a flat 4 cents per minute. Company C’s monthly charge is $25 with 5 cents per minute for the first 1000 minutes and 3.5 cents per minute beyond that limit. Which company should be selected to minimize the total monthly charge?

Question

21-11-2019
Mathematics

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A household uses at least 3000 minutes of long-distance telephone calls monthly and can choose to use the services of any of three companies: A, B and C. Company A charges a fixed monthly fee of $10 and 5 cents per minute for the first 1000 minutes and 4 cents per minute for all additional minutes. Company B’s monthly fee is $20 with a flat 4 cents per minute. Company C’s monthly charge is $25 with 5 cents per minute for the first 1000 minutes and 3.5 cents per minute beyond that limit. Which company should be selected to minimize the total monthly charge?

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Favouredlyf Favouredlyf · Answer 1 · 2019-11-29T17:37:52+01:00

Answer: Company C's services

Step-by-step explanation:

The household uses at least 3000 minutes of long-distance telephone calls monthly. We will assume that the household made more than 3000 calls monthly. Assuming the household made 5000 calls

1) if they use company A

Company A charges a fixed monthly fee of $10 and 5($0.05) cents per minute for the first 1000 minutes and 4($0.04) cents per minute for all additional minutes.

The fixed cost = $10

The first 1000 minutes = 1000×0.05= $50

4000 additional minutes = 0.04×4000 = $160

Total cost of 5000 minutes = 10 + 50 + 160 = $220

2)Company B’s monthly fee is $20 with a flat 4($0.04)cents per minute.

The fixed cost = $20

5000 minutes = 0.04×5000= $200

Total cost of 5000 minutes = 20 + 200 = $220

3) Company C’s monthly charge is $25 with 5($0.05)cents per minute for the first 1000 minutes and 3.5($0.035)cents per minute beyond that limit.

The fixed cost = $25

The first 1000 minutes = 1000×0.05= $50

4000 additional minutes = 0.035×4000 = $140

Total cost of 5000 minutes = 25 + 50 + 140 = $215

Since the household uses at least 3000 minutes, Company C's services should be selected to minimize the total monthly charge because it becomes cheaper as the number of minutes increases.