case study 4.docx - Sara Abouelniaj | A04178922 Case...

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2 Sara Abouelniaj | A04178922 Case Study #4: Planning an Advertising Campaign The decision variables are: T1= number of televisions advertisements with rating of 90 and 4000 new customers T2= number of television advertisements with rating of 40 & 1500 new customers R1= number of radio advertisements with rating of 25 & 2000 new customers R2= number of radio advertisements with rating of 15 & 1200 new customers N1= number of newspaper advertisements with rating of 10 & 1000 customers N2= number of newspaper advertisements with rating of 5 & 800 new customers The linear programming model and solution using The Management Scientific: MAX = 90T1 + 55T2 + 25R1 + 20R2 +10N1 +5N2 Subject to : 1. 1T1 < 10 2. 1R1 < 15 3. 1N1 < 20 4. 10,000T1 + 100,000T2 + 3,000R2 + 1,000N1 < 279,000 5. 4,000T1 + 1,500T2 + 2,000R1 + 1,000N1 + 800N2 > 100,000 6. -2T1 – 2T2 + 1R1 + 1R2 > 0 7. 1T1 +1T2 < 20 8. 10,000T1 + 100,000T2 > 140,000 9. 3,000R1 + 3000R2 <99,000 10. 1,000N1 + 1000N2 > 300,000 Optimal Solution: Objective Functional Value = 2,160.00 Objective Function Value =2,160.00 Variable Value Reduced Costs T1 10.00 0.000 T2 5.000 0.000 R1 15.000 0.000 R2 18.000 0.000 N1 20.000 0.000 N2 10.000 0.000 Constraint Slack/surplus Dual prices 1 0.00 35.00 2 0.00 5.000 3 0.00 5.000 4 0.00 0.006 5 27,100.00

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