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# page%20301 - TA 8 L E 20 Fitttlltlﬁ lltE[lttﬂl[ti...

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Unformatted text preview: TA 8 L E 20 Fitttlltlﬁ lltE [lttﬂl [ti LPUQ) [Bﬂﬂlénliﬂm max 2 T; C 7 I.) ll id max :- : 2A1 + \3 it i; + 3n st. .i'. + A": l in =-= 2 2n + .Y; “i“ \4 E 11 — x: -l- x}, E (i l—. .i'l, x; i 0. x3 urs, .\'4 S 0 The reader may verify that with these rules, the dual of the dual is always tho primal This is easily seen from the Table E4 format. because when you take the dual of" the dual you are changing the LP back to its original position. Group B duals of [lie lollowing Li’s: 5 This problem shows why the dual variable for an equality 2M _;_ \ constraint should be urs. . 7 \l T h i it Use the rules given In the text to ﬁnd the dual of" it — \3 E 3 max : - .\'l 2x; - s.t. it Now transform the LP in part (a) to the normal l‘orui Using (16) and (E7). take the dual of the [rat " armed LP, Use _i-§ and ﬁg as tlio dual variables for the two priw mat constraints derived from 2x, + I: — 5. u. I: Make the substitution __l‘3 : l; W ii; It] the part (in) answer. Now show that the two duals obtained in parts (a) and (ii) are equivalent. g-ﬂ E This problem shows why a dual variabici‘, corresponding ). 3 Using the rules given in the text, lint! the dual of" a. to a : constraint in a max problem must satis'l‘y 71‘, max : 1 3x; + _\‘~ SI, .l'l T " l3 Transform the LP ol‘ part (a) into a normal max problem. Now use (16) and (l?) to ﬁnd the dual ol' [lie transformed Li! Let If}; he the dual variable correspond- ing to the second primal constraint. (5 Show that, defining f; I jvgl the dual in part (a) is equivalent to the dual in part {b}. 6 . 5 Surﬁng the Hint at an LP ...
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