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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?

Short Answer

Expert verified
Bridget Ashton should choose her phone plans based on the long-distance calls she expects to make. For 100 minutes of long-distance calls, Plan A would be the most economical, costing $10. If 240 minutes of long-distance calls are expected, Plan B is the best option, costing $15. If she expects 540 minutes of long-distance calls, Plan C is the most economical, costing approximately $24.5.

Step by step solution

01

Understand and break down the phone plans

We have three phone plans to analyse: 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 Plan C - Pay a fixed monthly fee of $22 for up to 510 long-distance minutes and 5 cents per minute thereafter Now, we will write the equations for each plan.
02

Write the equations for each plan

Plan A: Total cost for Plan A = (10 cents/min) * (number of minutes) So the equation for Plan A is: \(C_A = 0.10m\) Plan B: Total cost for Plan B has two cases: - If the number of minutes (m) is less than or equal to 240, the cost is fixed at $15. - If the number of minutes (m) is more than 240, the cost is $15 plus 8 cents for each additional minute. So the equation for Plan B is: \(C_B = 15 + 0.08(m-240)\) for \(m > 240\) Plan C: Total cost for Plan C has two cases as well: - If the number of minutes (m) is less than or equal to 510, the cost is fixed at $22. - If the number of minutes (m) is more than 510, the cost is $22 plus 5 cents for each additional minute. So the equation for Plan C is: \(C_C = 22 + 0.05(m-510)\) for \(m > 510\) With these equations ready, we can create the graph.
03

Create the graph for the total monthly costs

Using the equations we found in step 2, we can create a graph with the number of minutes on the x-axis and the total monthly cost on the y-axis. For every number of minutes (m), plot the points in the graph for each plan's equation. You can use graphing software or graph by hand to visualize the total costs of the three plans.
04

Determine the best plan for specific minutes of use

We have 3 cases to consider. Case 1: 100 minutes of long-distance calls Using the equations we found: \(C_A = 0.10(100) = \$10\) \(C_B = \$15\) \(C_C = \$22\) Plan A is the cheapest option for 100 minutes. Case 2: 240 minutes of long-distance calls \(C_A = 0.10(240) = \$24\) \(C_B = \$15\) \(C_C = \$22\) Plan B is the cheapest option for 240 minutes. Case 3: 540 minutes of long-distance calls \(C_A = 0.10(540) = \$54\) \(C_B = 15 + 0.08(540-240) = \$39\) since \(m > 240\) \(C_C = 22 + 0.05(540-510) = \$24.5\) since \(m > 510\) Plan C is the cheapest option for 540 minutes. Conclusion: Bridget Ashton should choose Plan A if she expects to make 100 minutes of long-distance calls, Plan B for 240 minutes, and Plan C for 540 minutes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Variable Costs
When businesses analyze their expenses, understanding variable costs is crucial. Variable costs are the expenses that change in direct proportion to the volume of goods or services produced or sold. In the case of a long-distance phone plan, the variable cost component is the charge per minute of call. For example, Plan A from Bridget Ashton's options is a purely variable cost structure, charging 10 cents per minute with no fixed monthly fee.

As the number of minutes increases, the total variable cost also increases linearly - a critical concept for total cost analysis. This clear relationship can be graphically represented, making it easier to understand and predict expenses as volume changes. In real-world scenarios, these can include costs of materials, direct labor, and commission-based compensation.
Fixed Costs
In contrast to variable costs, fixed costs remain constant regardless of the level of production or business activity. These are expenses that don't fluctuate with sales volume or production rates, such as rent, insurance, or a salaried employee's wages. For Bridget Ashton's restaurant, phone Plans B and C include a fixed monthly fee, representing the fixed cost element of her long-distance phone service expenses.

The fixed cost provides stability in budgeting since it doesn’t change with activity levels. However, Ashton needs to understand that even if she doesn't use her phone service, she will still be accountable for these fixed charges. This underscores the importance of choosing the right plan based on expected usage to help control overall expenditures.
Total Cost Analysis
A total cost analysis involves summing up all the fixed and variable costs associated with a business activity to understand the complete financial picture. This holistic view of costs assists in making informed decisions that align with the financial goals of the organization. In Ashton's scenario, total cost equations for each phone plan are calculated considering both the fixed fee and the variable charges beyond a certain usage threshold.

As the total cost is influenced by the number of minutes used, Ashton must carefully forecast her usage to determine the most cost-effective phone plan. A thorough total cost analysis typically includes plotting costs against different levels of activity, enabling visualization of the least and most expensive options under various scenarios.
Cost-Volume-Profit Analysis
Finally, we touch upon the concept of cost-volume-profit (CVP) analysis, which is a financial tool used to understand how changes in cost and volume affect a company's operating profit. It's a powerful way to look beyond just the costs and to include revenue and profit perspectives. This form of analysis combines the elements of fixed and variable costs to determine the break-even point, or the level of sales needed for the business to be profitable.

In Bridget Ashton’s decision-making process, this type of analysis would encompass not only the costs of the different phone plans (as represented by the total cost analysis) but also how these costs interact with her restaurant’s revenue patterns. For businesses, including her potential restaurant, success means finding the balance where the volume of sales or business activity offsets the combined fixed and variable costs, leading to profit generation. In every scenario, understanding these concepts is fundamental to making strategic and profitable decisions.

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Most popular questions from this chapter

What is a cost driver? Give one example.

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