Homework 1 Solutions.pdf - Introduction to Optimization...

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Introduction to OptimizationMS&E 111/ENGR 62, Stanford UniversityInstructor: Ashish GoelHomework 1 SolutionsNote.We post that sharing these solutions with anyone will be considered a violation of the honor code.Problem 1Letx= [xAxB]Tbe the vector of pounds of feed types A and B. Also letcT= [1 2] be the vector of prices,b= [600 40]T, andA=5007005025.(a) The LP may be written asminimizecTxsubject toAxbxBxAx0(b) Please find the Excel file hw1prob1solution.xls.Problem 2Letxidenote the number of units for productito produce. Letb= [90 80]Tdenote the column vector ofassembly and testing hour capacities andcT= [9 8]-[1.2 0.9] = [7.8 7.1] denote the profit for each of theproducts. Finally, letA=1/41/31/81/3denote the required amounts of assembly and testing labor (rows) per product (columns).(a) The LP is given asmaximizecTxsubject toAxbx0.(b) We may introduce a new variablexoto denote the amount of overtime hours that we wish to purchase

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