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HOMEWORK 2: LINEAR PROGRAMMING APPLICATIONS • For this home work, you will need to submit both handwritten work and the output and from of a single PDF, bine multiple PDFs into one using free tools online or AdoEw which all UNC s:udents should this wig—t. mign to it easier to grade. • immb with m-ctly is requiæd In the Julia declare variables with the name giver. in the problern •men, after solving the problem, in of print all of all of in optimization as well the value of the '*jective function. • —t add —ts V7riablø, md *tive fm • E. it. In Outputs Of All Cells then Run All to that there are no • To genera a PDF 01 your — In the main dick Export (may be hidden behind a 3 dots menu) — Exp'M•t as PDF (my rBluire additional extensi.,ms)_ — If Exp«t PDF fails give file HTML this HTML file a web brcwser and save the HTML file as a PDF. If i— with this, fißt opal M'tebmks in just the notebook itself), then try expcming to PDE This often issues that may otherwise — If you get exporting to work in may a Jupyter Notebex»k to PDF con- 1 (35 points): of A. stutup wiut to off« its emp:oyees coming yeu_ In to keep the tisfied she to tisfy the iollcwing
• Tom Wants at least or Will quit; • Peter. Nina. md Smir at SIOR415 Introduction to - Fall 202 • Gary Wants his salary to be at least as high as the combined salary Of Tom and Peter; • Linda her salary to be than Gary; • The salary of Nina and Samir a t twice salary of and salary is a t least as that Of Peter and a t least as high as that Of The combined Of Bob and Peter Should be at least • Linda Should not make more than the combined salary Of and Tom. a) Write LP tlut will mployæ of A these constraints while minitnizing the total salary satisfy of b) Write an LP that will determine the for the of that satis$' of while minimizing of t paid —oyee. c) mte a titled impl—nt put b. In Julia variables for each person's salary as as the variables needed to reformulate min. into a md this a To your solution, the optimal objective is 68S(X)_
and then declare a variable x Which is indexed over types and blends. Create dictionaries indexed which of wailable, pric., the coffee Then, define all Of the the obÉctive function. An example cemstrai_nt that x is indexed 'wer the JuMP is called *Robust least 60 To check that you correctly implen•wnted this problem, the maximum profit is A shopping mall Hill is Wts mix its f.uility. Stm-w of i Ewing different i, Each sector will have at area A (in thousands of square feet) and funds (dollars foot) aside "finishing* of stm of typ i, From prior experience, the developer can estimate the present worth of from a i store j th requird (in of a type i store, requires: (i) having and N, of each type i; (ii) having a fi md Fi of fæt) to stcm of type md , (iii) a budget of b (dollars) for finishing costs. that the number of each Of store does not to integer Use the S to set of all tyFS of md C to all a) Formulate a linear program to find an optimal tenant mix that will maximize total worth b) mall irw—tigate pr—t mth in Tht is, shopping to lomt pmt (pmfit) of fm (a) to this new *tiv e. Ycm only need to list
