Variable costs, fixed costs, total costs. Bridget Ashton is...

Variable costs, fixed costs, total costs. Bridget Ashton is getting ready to open a small restaurantt She is on a tight budget and must choose between the following long-distance phone plans: Plan A: Pay 10 cents per minute of long-distance calling Plan B: Pay a fixed monthly fee of \$15 for up to 240 long-distance minutes and 8 cents per minute thereafter (if she uses fewer than 240 minutes in any month, she still pays S15 for the month) Plan C: Pay a fixed monthly fee of \$22 for up to 510 long-distance minutes and 5 cents per minute thereafter (i she uses fewer than 510 minutes, she still pays $\$ 22$ for the month). 1. Draw a graph of the total monthly costs of the three plans for differentlevels of monthly long-distance calling. 2. Which plan should Ashton choose if she expects to make 100 minutes of long-distance calls? 240 minutes? 540 minutes?

Variable costs, fixed costs, total costs. Bridget Ashton is getting ready to open a small restaurantt She is on a tight budget and must choose between the following long-distance phone plans:
Plan A: Pay 10 cents per minute of long-distance calling Plan B: Pay a fixed monthly fee of \$15 for up to 240 long-distance minutes and 8 cents per minute thereafter (if she uses fewer than 240 minutes in any month, she still pays S15 for the month) Plan C: Pay a fixed monthly fee of \$22 for up to 510 long-distance minutes and 5 cents per minute thereafter (i she uses fewer than 510 minutes, she still pays $\$ 22$ for the month).
1. Draw a graph of the total monthly costs of the three plans for differentlevels of monthly long-distance calling.
2. Which plan should Ashton choose if she expects to make 100 minutes of long-distance calls? 240 minutes? 540 minutes?

Key Concepts

Graphing Cost Functions

Graphing cost functions involves plotting the total cost against usage levels to visually compare different pricing plans. By identifying fixed cost baselines, variable rate segments, and points where the cost structure changes, one can clearly see which plan is more economical at various usage levels. This graphical analysis is a helpful tool in decision-making processes related to cost optimization.

Piecewise Functions

Piecewise functions are used to model situations where the cost structure changes based on different intervals of usage. In the given problem, phone plans that offer a fixed fee up to a limit and then charge an additional per-minute rate can be represented as piecewise functions. This concept is key for accurately graphing the total cost and understanding breakpoints in pricing.

Total Costs

Total costs are the sum of both fixed and variable costs. This combined cost function helps analyze how different pricing structures perform based on usage levels, indicating the overall expense incurred each month. It is crucial to calculate and compare total costs when evaluating different service plans to determine the most cost-effective option.

Variable Costs

Variable costs fluctuate with the level of usage. For phone plans, this represents the cost per minute charged when the usage exceeds a certain limit or in plans that do not include a base allowance. It is important to understand how these costs add up as the usage increases and how they complement or substitute the fixed costs in determining the overall expenditure.

Fixed Costs

Fixed costs are expenses that do not change with the level of usage or production. In the context of the phone plans, fixed costs refer to the flat monthly fees that a customer must pay regardless of the number of minutes used. These costs are incurred even if no usage takes place and provide the baseline expense in the total cost calculation.

Transcript

00:01 We're told that bridget is getting ready to open a small restaurant and she's on a tight project.

00:06 So she must choose between the following long distance phone plans.

00:10 The plan a is that she pays 10 cents per minute of long distance calling.

00:20 10 cents per minute of long distance calling.

00:32 The plan b is that she pays a fixed monthly fee of $15.

00:39 So this is fixed right for up to 240 long distance for 240 long distance minutes and 8 cents per minute right if she uses fewer than 240 minutes in any month she'll pay 15 for the month so she's going to pay 15 for every month for 240 minutes if she is more than that they should pay 8 cents per minute after and the plan c is that she's going to pay a fixed monthly fee of $22 for up to 520 long distance minutes and 5 .5 per minute after.

01:39 So now, first question wants us to draw a graph of the total monthly cost of the three plans for different levels of monthly long distance calling.

01:50 So for the question for the first question let x let x be the number of meanings required between plan a and b so we can see since plan a and plan b have equal cost right we can say that 0 .10 which is the same x equals to $15 on then we can say that x is equal to 15 plus no rather divided by 0 .10 and then x equals to 150 minutes so this is the minute right so let's so we're going to let why be the number of minutes required between plan b and c between plan b and c now since plan b and c have equal cost we can say that $15 plus eight cents open brackets y minus two 40 is equal to 22 and then 0 .8 cents y minus 240 is equal to 22 minus $15 and then y minus 240 is equal to 7 divided by 0 .08 and then y is equal to 87 .85 plus 240 so y is equal to minutes right so based on the calculation we have done we can prepare the table that shows the number of minutes about months for all the plans and we take the table should look like this with the minutes per month i'm going to do mp mp so this is the minute and then we have plan a we have and is in dollars per month we have plan b we have plan c so for zero minutes for a we're going to have dash dollars for b is going to be $15 and for c is $22 for 50 minutes so we have $5 here we have $15 here we'll have $22 because remember what the requirement said that we can make on calls for up to um for up to 20 minutes monthly for 15 for b and for c five 10 minutes for 22 monthly so that i'm getting that and a b and c is in dollars this is a minute so for hundred minutes we're gonna have ten dollars a 15 for b and still 15 and still 22 for c so for one 50 minutes we're gonna have 15 year 15 year and 22 yes 22 now for 200 minutes gonna have 20 year 15 year 15 year 22 year now for for 240 minutes because that's why there's a change for 240 minutes we're going to have 24 year 15 here and 22 year now for 300 minutes we're going to have 30 19 .80 and we're going to have 22 year for 327 .5 minutes we're going to have 32 point seven five we're gonna have 22 and we're gonna have 22 here now for three 15 minutes we're gonna have 35 we're gonna have 23 .80 we're gonna have 22 for 400 minutes we're gonna have 40 we're gonna have 27 .80 we're gonna have on 22 for 450 we're going to have 45 31 .80 and 22 and for 510 we're going to have 51 .60 and 22.

07:29 Now for 5 .10 we're going to have 51 30 .60 and 22.

07:36 Now for 540 we're going to it's just going to keep being the same requirement according to the question.

07:43 Like according to what the question gives us.

07:45 So this is what the table should look like.

07:47 And then based on the figure we can prepare a graph that shows the number of long distance minutes and the total cost and that should look like this so the total cost to be right here and the number of long of minutes right here and then we're going to have year from zero to 60 and year from 100 to 600 and basically um the plan a is basically going to be a straight graph i might not draw exactly but you follow what the table shows you.

08:54 It's going to be a straight graph and this is plan a...

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