RQLT Task 2 Revision 2: Graph Of The Equation The Candidate

Rqlt Task 2 Rev 2graph Of The Equation The Candidate Accurately Gr

RQLT Task 2 rev 2 Graph of the Equation - The candidate accurately graphs the equation, with limited detail. The graph has improved. The necessary descriptive labeling for each axis could not be located. Please revise the graph as needed.

RQLT Task 3 rev 2 A3a2. Savings After 23 Months - The candidate does not accurately determine which plan yields the greatest balance if the person stops saving after 23 months. Plan B is incorrect.

A4. Relevant Quadrants - The candidate provides a logical explanation, with insufficient detail, of which quadrant(s) of the graph is(are) relevant. Quadrant 1 is correct. The current response lacks sufficient detail to meet the requirements for this question.

QLT Task 5 rev 1 C. Graphical Representation of Cost Options - The candidate provides an accurate graphic depiction of the real-world problem, with no detail, using appropriate graphing software. The graph is correct but a descriptive label is required for the y-axis.

D. Decision-Making Process - The candidate provides a logical discussion, with no support, of a decision-making process that is based on both mathematical reasoning and non-financial, or situational, considerations. No decision-making process was described other than the statement that the "point where the two Plans will be equal (25, 300), after this point it will be better for Joe to choose Plan 300" but other factors may be necessary when determining the final customer recommendation.

D1. Final Recommendation - The candidate does not provide a logical discussion of the final recommendation that states the option that most closely meets the consumer’s financial needs and non-financial considerations. No clear and decisive final recommendation is evident in the work submitted. The recommendation should clearly meet the needs of the customer.

Paper For Above instruction

The problem at hand involves helping Joe, a newly hired employee, determine the most cost-effective cell phone plan based on his expected usage and financial constraints. Joe's employer offers him two options: Plan 250 and Plan 300. Ensuring an optimal choice requires analyzing the cost structures of both plans, graphing their cost functions, and considering both mathematical specifics and situational factors to provide a comprehensive recommendation.

Joe receives an allowance of $300 from his company, which he can spend or save as long as his communication needs are not affected. Plan 250 costs $250 monthly and includes 20 hours of voice messaging and unlimited texts. Additional voice messaging beyond 20 hours costs $10 per hour. Conversely, Plan 300 costs $275 monthly with unlimited calls and texts, and no additional charges. Joe's expected usage is between 20 and 30 hours of voice messaging per month. To aid his decision, we analyze the costs associated with each plan as a function of voice call hours, graph these functions, and identify the break-even point where both plans cost the same.

The cost function for Plan 250 can be expressed mathematically as follows: if x represents the hours of voice messaging used in a month, then the total monthly cost y is:

  • y = 250, for x ≤ 20
  • y = 250 + 10(x - 20), for x > 20

This piecewise function reflects the fixed cost up to 20 hours, with additional charges for extra usage. Conversely, Plan 300 maintains a flat rate of $275 regardless of usage, making its cost function straightforward: y = 275.

To determine the break-even point where both plans cost the same, set the functions equal:

250 + 10(x - 20) = 275

Simplifying the equation:

250 + 10x - 200 = 275

10x + 50 = 275

10x = 225

x = 22.5 hours

This indicates that beyond 22.5 hours of voice messaging, Plan 300 becomes more economical for Joe. To visualize these functions, we can graph both cost functions over the relevant range (0–30 hours). The graph reveals that for usage up to approximately 22.5 hours, Plan 250 is less costly, aligning with Joey's anticipated 20–30 hours of use.

In constructing the graph, the x-axis represents hours of voice messaging, while the y-axis shows the corresponding monthly cost in dollars. The graph of Plan 250 is a piecewise linear function: flat at $250 up to 20 hours, then increasing at a rate of $10 per additional hour. The graph of Plan 300 is a straight line at $275 for all usage levels. The point where these lines intersect at (22.5, approximately $275) indicates the break-even threshold.

Beyond the mathematical analysis, decision-making should consider other situational factors. Since Joe’s expected usage is between 20 and 30 hours, and he has a $300 budget, both plans generally fit within his allowance. If Joe's usage stays below 22.5 hours, Plan 250 saves him money; above that, Plan 300 is more suitable. However, other considerations, such as the convenience of unlimited calls/texts in Plan 300, potential future usage increases, and the ease of billing, might tip the decision toward Plan 300 for greater flexibility and simplicity.

In conclusion, based on the graphical and algebraic analysis, Joe should opt for Plan 250 if his voice messaging remains below 22.5 hours. Should his usage approach or exceed this point, Plan 300 provides better financial value. Considering his current usage estimates and the importance of simplicity, a final recommendation could favor Plan 300, especially if there is uncertainty or potential for increased usage, as the flat rate offers predictability and unlimited services. This decision balances mathematical insights with practical, situational considerations, aligning financial efficiency with Joe’s needs.

References

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  • Moore, R. (2020). Understanding Financial Decision-Making. Journal of Financial Planning, 33(2), 45-52.
  • Reid, S. (2019). Graphing Techniques for Business and Economics. Pearson Education.
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