Linear programing Case Study Peter.docx - 1 Formulate the Linear Problem model for this problem We first define the different variables in this scenario

# Linear programing Case Study Peter.docx - 1 Formulate the...

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1. Formulate the Linear Problem model for this problem We first define the different variables in this scenario we use (X) as a nomenclature for the different nail polish, it is necessary to come with the following proposition: X 1 is the bottles of fire red nail polish X 2 Bright red nail polish X 3 Basil Green nail polish X 4 Basic pink nail polish pink nail bottles combined which is at least 50 bottles. a.)- Building the linear model Max (Z) : 100x 1 +120x 2 +150x 3 +125x 4 Subject to: x 1 +2x 2 +2x 3 +2x 4 ≤ 108 Display space in units 3x 1 +5x 2 +0x 3 +x 4 120 Time to set up the display 1x 1 +x 3 25 Max (D) for fire red &Green Polish X 2 +x 3 +x 4 50 Min (D) for bright red, green & pink nail x 1 , x 2 , x 3 , x 4 0 b.)- The Optimal solution is \$7475 (QM & Excel) the beauty salon can maximize their sale and gain \$7475. This solution is the maximum gain from the total profit function (Z). It is a feasible solution in this case, since this is a maximization problem. To make sure the results are true, I compute both solutions in excel first and verified it in

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