InClassCase3 - ParketsisterKey

# InClassCase3 - ParketsisterKey - OSCM 230 LP Case Study:...

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OSCM 230 Management Science LP Case Study: Parket Sisters Professor Dong Parket Sisters Linear Programming Formulation: MAX: 3.0 X 1  + 3.0 X + 5.0 X 3 Subject to:   Plastic:    1.2 X 1  + 1.7 X + 1.2 X  1,000 Chrome:  0.8 X 1  +    0 X 2  + 2.3 X 1,200                                             Stainless Steel: 2.0 X 1  +  3.0 X 2  + 4.5 X 2,000 X 1  , X 2  , X 3    0 X = number of ballpoint pens X = number of mechanical pencils X = number of fountain pens The Excel spreadsheet setup: 1

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OSCM 230 Management Science LP Case Study: Parket Sisters Professor Dong The Answer report: Microsoft Excel 9.0 Answer Report Worksheet: [Parketsister.xls]Sheet1 Target Cell (Max) Cell Name Original Value Final Value \$F\$6 Objective Function Profit 0 2766.666667 Adjustable Cells Cell Name Original Value Final Value \$C\$4 Ballpoint pens  (X1) 0 700 \$D\$4 Mechanical pencils  (X2) 0 0 \$E\$4 Fountain pens  (X3) 0 133.3333333 Constraints Cell Name Cell Value Formula Status Slack \$F\$9 Plastic LHS 1000 \$F\$9<=\$H\$9 Binding 0 \$F\$10Chrome LHS 866.6666667 \$F\$10<=\$H\$10 Not Binding 333.3333333 \$F\$11Stainless Steel LHS 2000 \$F\$11<=\$H\$11 Binding 0 The sensitivity report: Microsoft Excel 9.0 Sensitivity Report Worksheet: [Parketsister.xls]Sheet1 Adjustable Cells     Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease \$C\$4 Ballpoint pens  (X1) 700 0 3 2 0.777777778 \$D\$4 Mechanical pencils  (X2) 0 -1.383333333 3 1.383333333 1E+30 \$E\$4 Fountain pens  (X3) 133.3333333 0 5 1.75 2 Constraints     Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease 2
OSCM 230 Management Science LP Case Study: Parket Sisters Professor Dong \$F\$9 Plastic LHS 1000 1.166666667 1000 200 466.6666667 \$F\$10 Chrome LHS 866.6666667 0 1200 1E+30 333.3333333 \$F\$11 Stainless Steel LHS 2000 0.8 2000 555.5555556 333.3333333 1)  The optimal weekly product mix is: 700 ballpoints, 0 pencils, and 133.33 fountain pens.  We  could round the fountain pens off to 133, but we shall not, in order to avoid rounding  problems.  The profit is \$2,766.67. 2) 3) Yes, the answer is unique.  There is no zero in the allowable increase and allowable  decrease of adjustable cells.  4)  The marginal values for one more unit of each of the resources are: \$1.17 for plastic, 0 for  chrome, and \$0.80 for stainless steel.  These are the shadow prices for our three resources. 5)  Because 500 is less than the maximum allowable increase of 555.56 ounces, the shadow

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## InClassCase3 - ParketsisterKey - OSCM 230 LP Case Study:...

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