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?

Answer: Company C's servicesStep-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 = $10The first 1000 minutes = 1000×0.05= $504000 additional minutes = 0.04×4000 = $160Total cost of 5000 minutes = 10 + 50 + 160 = $2202)Company B’s monthly fee is $20 with a flat 4($0.04)cents per minute.The fixed cost = $205000 minutes = 0.04×5000= $200Total cost of 5000 minutes = 20 + 200 = $2203) 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 = $25The first 1000 minutes = 1000×0.05= $504000 additional minutes = 0.035×4000 = $140Total cost of 5000 minutes = 25 + 50 + 140 = $215Since 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.