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Minimum sum of abssolute values & Min max of abssolute values

Hi,

I need help with the following problem linear programming question that asks for two linear programming solutions for a timer series that Min sum of abs values & Min max of abs values. I have attached the detailed questions in the attached Word document. I have already solved question 1, which is attached in an Excel file, so I need assistance with questions 2 through 4. Please note that you cannot use the "abs" function in Excel to solve.

I have also attached a snapshot of an US Naval Academy paper that addresses linear methods to solve Min sum of abs values & Min max of abs values. Unfortunately, I am still not able to decipher solutions.

Can you please help?

Thanks,
Sunny

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Week(t) Sales(t)
1 17
2 21
3 19
4 23
5 18
6 16
7 20
8 18
9 22
10 20
11 15
12 22

**** I already completed question 1 *****
1) Use ordinary least squares for forecasting. Generate the regression equations: sales(t) = a +bt by using the data analysis add-in in Excel. You will generate values for a and b such that the sum of squared errors is a minimum. That is, the sum from t=1,â?¦..12 of (sales(t)-sales(t))^2 is a minimum. The least squares formula that is used is derived from differential calculus and the a,b found are such that the sum of squared errors can be no smaller with any other values for a and b.
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*** I need help with the below 3 questions. ***

2) Find values for a and b for the same time series such that you minimize the sum from t=1,â?¦..12 of |sales(t)-sales(t)|. To do this you must formulate a linear program. Thus you may not use the â??absâ? function in Excel. Create/solve the model in Excel and also write down the linear program in algebraic form.

3) Find values for a and b for the same time series such that you minimize the maximum (overall t=1,â?¦..12) |sales(t) â?" sales(t)|. To do this you must formulate a linear program. Thus you may not use the â??absâ? function in Excel. Create/solve the model in Excel and also write down the linear program in algebraic form.

4) Comment on the use of these three different objectives in questions 1,2, and 3 and why a company might use each of the three objectives.

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Solution Summary

Minimum sums of absolute values and minimum maximum of absolute values are examined.

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