Lecture5

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Unformatted text preview: - 2, + 8.~, 5 ? 5, + 2X. + 3X, + 4.Y, 5 I l The problem in standard form is v, X) \-, Y, 2 0 EM-602 I QM-710 (NJ) Lecture 5 Page 5-3 Homework Problem 35 Homework Problem 3-22 (solution) 4 6! ct=-= lj 2!4! Solve by M-Technique (a ) Maximize z=Zx, +3x, -5x, (d) Minimize z = 4x, - 8.5 + 3.5 subject to s, +2x, +s, =7 2.x, -5x? +.K, t 10 x,,.~*>x, 20 b) ffnd all bask solutions and their feasibility by enumeration (see handout) c) Restrict to only feasible solutions and choose the extreme point with the optimal 2 (8,0,3,&Q, 0) L = 31 Homework Problem 3-22 Sensitivity Analysis (solution) (a) Masimize 2 = Z.r, +3x2 - 5.r, - .W?, - .W+ ct. I, +2.~~ +I, +R, = I Given an optimal simplex tableau, we can immediately conclude: Decision Variables and their optimal values Objective Function value Scarcity or Abundance of Resources Unit Worth I Shadow Prices I Dual values l 5, -5x, +.Q -s, +R, = IO -- x,.x2..r,_R,.s,.R. 20 r-(:!+3.\f)s, -(3-l.\f).r, -(-j+L\/).r, +.\h, = -1741 R, = 7:R? = Io..Y,..K:.X,.S, =0 . l l l Sensitivity Analysis Sensitivity Analysis (Changes in Constraint RHS) (Changes in Objective Coeffkient) How much can constraint associated with slack (or surplus) variable SII change? Augment RHS of resource n by amount Dn Calculate resulting change in RHS for each bask row (including t) according to: New RHS = Old RHS + Dn x (Co1 entry under sn) Find the most restrictive range of Dn for which the RHS of every basic row remains ,g Case 1 - Change in the Objective Coefficient for a variable that is basic in the optimal tableau Augment the coefffcient of Basic variable xn by adding the amount dn Compute the new z-row according to: New zentry = Old z-entry + dn x (Co1 entry under zn) (except, if old zsntry was 0, leave it at 0) Find the most restrictive range of dn for which the zentries remain 2 0 l l l l l l EM-602 I QM-710 (NJ) Lecture 5 Page 5-4 Sensitivity Analysis Problem 3-39 (Changes in Objective Coefficient) Case 2 - Change in the Objective Coefficient for a Non-basic variable in the optimal tableau Augment the coefhcient of Non-Basic variable xn by adding the amount dn Compute the new zentry for the Nonbasic variable according to: New zentry = Old zentry - dn Find the range of dn for which the zentry remains > 0 Consider the following LP allocation model: l Maximize z = 3-y, + 2.~~ (profit) subject to 4x, + 3.5 < 12 (resource 1) 4x, +x2 I 8 (resource...
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This document was uploaded on 03/31/2014 for the course MS 602 at NJIT.

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