Your company offers three cell phone plans. The details are below:
Plan A allows 450 minutes for $39.99 with .25/minute for each minute over 450.
Plan B allows 900 minutes for $59.99 with .30/minute for each minute over 900.
Plan C allows 1500 minutes for $99.99 with .35/minute for each minute over 1500.
Write a report detailing the following:
An equation or inequality to represent each plan above.
Determine for how many minutes each plan is the best option for two customers. Customer Smith uses roughly 750 minutes per month. Customer Jones uses roughly 1350 minutes per month. Which plan should they choose and why?
Include a detailed explanation of your work, which scenario is better, and why.
Write a summary paragraph for your employees that will be answering and making phone calls.
A(m) = 39.99 for m <= 450
A(m) = 39.99 + 0.25(m-450) for m > 450
and similar functions for B,C
Now plug in m=750 and 1350 and check A,B,C to find the best
1. Equations or inequalities to represent each plan above:
- Plan A: Cost = 39.99 + (number of minutes - 450) * 0.25, where number of minutes > 450.
- Plan B: Cost = 59.99 + (number of minutes - 900) * 0.30, where number of minutes > 900.
- Plan C: Cost = 99.99 + (number of minutes - 1500) * 0.35, where number of minutes > 1500.
2. Calculating the cost for each plan based on the usage of two customers:
- For Customer Smith who uses roughly 750 minutes per month:
- Plan A: Cost = 39.99 (as 750 minutes are within the 450-minute limit).
- Plan B: Cost = 59.99 (as 750 minutes are within the 900-minute limit).
- Plan C: Cost = 99.99 (as 750 minutes are within the 1500-minute limit).
Therefore, all plans cost the same for Customer Smith, but Plan A is the most suitable choice as it offers sufficient minutes within the base price.
- For Customer Jones who uses roughly 1350 minutes per month:
- Plan A: Cost = 39.99 + (1350 - 450) * 0.25 = 39.99 + 225 * 0.25 = 39.99 + 56.25 = 96.24.
- Plan B: Cost = 59.99 (as 1350 minutes are within the 900-minute limit).
- Plan C: Cost = 99.99 + (1350 - 1500) * 0.35 = 99.99 - 150 * 0.35 = 99.99 - 52.50 = 47.49.
Therefore, Plan C is the most cost-effective choice for Customer Jones, as it offers more minutes for a lower cost compared to Plan A.
3. Summary paragraph for employees answering and making calls:
Dear employees,
We offer three cell phone plans to our customers: Plan A, Plan B, and Plan C. Each plan has different price points and offers different minute allowances. For customers who use roughly 750 minutes per month, Plan A is the best option as it provides sufficient minutes within the base price. However, for customers who use roughly 1350 minutes per month, Plan C is the most cost-effective choice, as it offers more minutes for a lower cost compared to Plan A. As you answer and make calls, please consider the specific needs and usage patterns of our customers to provide them with the most suitable plan.
Thank you for your dedication and excellent customer service.
Best regards,
[Your Name]
To represent each plan, we can use the following equations/inequalities:
Plan A:
Cost (A) = $39.99 + $0.25 * minutes, where minutes is the number of minutes used.
Plan B:
Cost (B) = $59.99 + $0.30 * minutes, where minutes is the number of minutes used.
Plan C:
Cost (C) = $99.99 + $0.35 * minutes, where minutes is the number of minutes used.
Let's calculate the cost for each plan based on the usage of Customer Smith and Customer Jones.
For Customer Smith (750 minutes):
Plan A cost = $39.99 + $0.25 * 750 = $39.99 + $187.50 = $227.49
Plan B cost = $59.99 + $0.30 * 750 = $59.99 + $225.00 = $284.99
Plan C cost = $99.99 + $0.35 * 750 = $99.99 + $262.50 = $362.49
For Customer Jones (1350 minutes):
Plan A cost = $39.99 + $0.25 * 1350 = $39.99 + $337.50 = $377.49
Plan B cost = $59.99 + $0.30 * 1350 = $59.99 + $405.00 = $464.99
Plan C cost = $99.99 + $0.35 * 1350 = $99.99 + $472.50 = $572.49
Based on the calculations, for Customer Smith, Plan A is the best option with a cost of $227.49. For Customer Jones, Plan A is still the best option with a cost of $377.49.
In summary, both Smith and Jones should choose Plan A as it offers the lowest cost for their respective usage. As employees who answer and make phone calls, it would be advisable to recommend Plan A to customers who use around 750-1350 minutes per month to ensure they get the best value for their money.