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### Problem Set 1

Course: ORIE 3310, Spring 2009
School: Cornell
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Word Count: 240

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3300/5300 ORIE Prof. Bland Problem Set 1 Fall 2009 Due: never This very short problem set is a continuation of Recitation Exercise 1. It will not be collected, but you should work these 2 problems and write out your solutions. Please complete problem 2 before the 9/8 lecture. Please complete problem 3 before the 9/10 lecture. Problems labeled numbers 2 and 3 below refer back to problem number 1 from the...

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3300/5300 ORIE Prof. Bland Problem Set 1 Fall 2009 Due: never This very short problem set is a continuation of Recitation Exercise 1. It will not be collected, but you should work these 2 problems and write out your solutions. Please complete problem 2 before the 9/8 lecture. Please complete problem 3 before the 9/10 lecture. Problems labeled numbers 2 and 3 below refer back to problem number 1 from the Recitation Exercise. 2. (a) In part 1(i) you worked with the brew new.dat data and found that the output from display Scarcity has values 1.32353 for corn, 0 for hops and 0.258824 for malt. Calculate the sum over the three scarce resources of the product of the value above times the availability of that resource (1.32353 600 + 0 480 0.258824 + 1200). Compare (to three decimal places) this value with the optimal objective function value (which you found in part (e(ii)) for this version of the brewery problem. (b) Repeat for the versions of the brewery problem examined in parts 1(a), 1c(i) and 1(d). 3. (a) Make an accurate drawing of the feasible region, the set of all feasible production programs (xA , xB ) for the brewery problem of part 1(a). (For shorthand here, I am asking you to denote by (xA , xB ) the pair (M ake(ALE), M ake(BEER)) from the AMPL solution.) Use graph paper or a drawing program that allows for similar accuracy. (b) On the figure from part 2(a) label all of the optimal solutions that you encountered in part 1(b) (your list from 1(b)(iv)).
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