For my class you have to choose from several different scenarios, make up your own equations from the scenario, and then solve and graph them in excel. I have chosen the following scenario:
Evaluate whether a prepaid or monthly cell phone plan is most effective for a customer that uses x weekday minutes per month.
I can do the math part of the problem myself, the part I am having trouble with is coming up with the equations. It is worded in the problem like this:
Develop an algebraic equation with clearly defined variables to represent the cost/yield of each option.
We are aloud to make up any numbers that we want.
To develop an algebraic equation to represent the cost/yield of each option, you need to define variables based on the given scenario and the specific attributes of each option (prepaid or monthly).
Let's start with the prepaid option.
1. Prepaid option:
Let's assume that the prepaid plan has a fixed monthly cost, let's call it C_prepaid. This cost would typically cover a certain number of weekday minutes, let's call it M_prepaid.
To represent the cost/yield of the prepaid option, you can use the following equation:
Cost_prepaid = C_prepaid
Since the prepaid plan has a fixed cost, the yield can be represented by the number of weekday minutes used, x, which is the variable provided in the scenario:
Yield_prepaid = x
Therefore, the algebraic equation for the prepaid option would be:
Cost/Yield_prepaid = C_prepaid/x
2. Monthly option:
Assuming the monthly plan also has a fixed monthly cost, let's call it C_monthly. However, this plan typically includes a certain number of weekday minutes, let's call it M_monthly. If the user exceeds this limit, they might incur additional charges.
To represent the cost/yield of the monthly option, you need to consider two cases:
a) If the user stays within the included weekday minutes:
The cost would still be the fixed monthly cost, C_monthly, and the yield would be the number of weekday minutes used, x:
Cost_monthly = C_monthly
Yield_monthly = x
b) If the user exceeds the included weekday minutes:
In this case, there would be additional charges, represented by a per-minute rate, let's call it R_per_minute. The yield would still be the number of weekday minutes used, x, but the cost would include the fixed monthly cost, C_monthly, plus the additional charges for the exceeded minutes (x - M_monthly) multiplied by the per-minute rate:
Cost_monthly = C_monthly + R_per_minute * (x - M_monthly)
Yield_monthly = x
Therefore, the algebraic equation for the monthly option would be:
Cost/Yield_monthly = Cost_monthly/Yield_monthly
Remember, these equations are just one way to represent the cost/yield relationship for each option. You can modify and adjust them based on your specific requirements and assumptions. Make sure to substitute the appropriate values for the variables (e.g., C_prepaid, C_monthly, M_prepaid, M_monthly, R_per_minute) when solving and graphing the equations in Excel.