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# hmk_3_s - ESE304 Introduction to Optimization(Homework#3...

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ESE304 - Introduction to Optimization (Homework #3) Fall Semester, 2010 M. Carchidi –––––––––––––––––––––––––––––––––––– Problem #1 (30 points) Consider the Dorian Auto problem (Example #2 in Chapter 3 of the text). a.) (5 points) Find the range of values on the cost of a comedy ad for which the current basis remains optimal. b.) (5 points) Find the range of values on the cost of a football ad for which the current basis remains optimal. c.) (5 points) Find the range of values for required HIW exposures for which the current basis remains optimal. Determine the new optimal solution if 28 + million HIW exposures are required and the range of values for for which this new optimaal solution remains optimal. d.) (5 points) Find the range of values for required HIM exposures for which the current basis remains optimal. Determine the new optimal solution if 24 + million HIW exposures are required and the range of values for for which this new optimaal solution remains optimal. e.) (5 points) Find the shadow price associated with each constraint. f.) (5 points) If 26 million HIW exposures are required, determine the new optimal z -value. This is Problem #4 on page 231 of the text: Operations Research by Wayne L. Winston. Problem #2 (25 points) Rad iocomanu facturestwotypeso frad ios .Theon lyscarceresourcethatis needed to produce radios is labor. At present, the company has two laborers, Laborer 1 is willing to work up to 40 hours per week and is paid \$5 per hour.

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Laborer 2 will work up to 50 per week for \$6 per hour. The price as well as the resources required to build each type of radio are given in the following table Radio 1 Radio 1 Radio 2 Radio 1 Price Resource Required Price Resource Required \$25 Laborer 1: 1 hour \$22 Laborer 1: 2 hours Laborer 2: 2 hours Laborer 2: 1 hour Raw Material Cost: \$5 Raw Material Cost: \$4 Letting x i be the number of Type i ( i =1 , 2 )rad iosproducedeachweek , that Radioco should solve the following LP. max z =3 x 1 +2 x 2 (Objective Function) s.t. x 1 x 2 40 (Laborer 1 Constraint) 2 x 1 + x 2 50 (Laborer 2 Constraint) x 1 ,x 2 0 (Sign Restrictions) a.) (5 points) For what values of the price of a Type 1 radio would the current basis remain optimal? b.) (5 points) For what values of the price of a Type 2 radio would the current basis remain optimal? c.) (5 points) If laborer 1 were willing to work only 30 hours per week, then would the current basis remain optimal? Find the new optimal solution to the LP is the current basis does not remain optimal. d.) (5 points) If laborer 2 were willing to work up to 60 hours per week, then would the current basis remain optimal? Find the new optimal solution to the LP is the current basis does not remain optimal. e.) (5 points) Find the shadow price of each constraint.
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hmk_3_s - ESE304 Introduction to Optimization(Homework#3...

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