Lecture5

profit subject to 4x 35 12 resource 1 4x x2 i

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Unformatted text preview: 2) 4x, - .v? I8 (resource 3) .x,,.r, 20 l l l Problem 3-39 (cont’d) Problem 3-39 l l l l l Determine from the optimal tableau the following: (a) Status of each resource (b) Unit worth of each resource (c) Resource with the highest priority for increase (d) Maximum change in availability of first resource to keep current solution basic l l l l Problem 3-39 Optimal Tableau Basic L K, 0 4 0 us 5/0 4 O ’ l/2 xl 1 0 0 0 -l/0 1 *!I Problem 3-39 (solution) 5 Soin l/0 0 17/2 -l/2 0 -2 (g) Maximum change in proftt coefficient for XI that will keep the solution optimal (h) repeat part (g) for x2 (a),(b),(c) Status & worth of resources K+ 3/a (a) repeat (d) for the second resource ~~,~~iated change in optimal 2 0 1 (a) Resources 1 and 2 have slacks that = zero, therefore both are scarce resource 3 has slack of 4 units therefore it is abundant (b) Shadow prices for resource 1, 2, 3 are 518, l/8,0 (respectively) in units of output per unit of additional resource (c) if ail costs are equal, give additional increase priority to resource 1 2 3/2 4 EM-602 / QM-710 (NJ) Lecture 5 Page 5-5 Problem 3-39 (solution) Problem 3-39 (solution) (d) maximum change in 1 st resource (e) maximum change in 2nd resource Problem 3-39 (solution) (g) change in profft of Problem 3-39 (solution) (f) effect of change on L value XI Let the coefficient of.5 become C, = . IfDc=12,thenz=l712+(12)(518)=16 If DC = 4, then L = 1712 + (4)(W) = 6 If Dz = 2, then L = 1712 + (2)(118) = 7018 If02=4,thenz=1712+(4)(1/8)=8 3 *d The z - row entry underx, is i - $ l l 13d The z- row entry anderx, is 8 + 7 l Thez-row’s RHS becomes y+y Therefore. d I 5 and d 2 - i Sensitivity Analysis Special Cases in LP’s (Reduced Costs) l l l l or. i 5 c, 2 8 Several Special Cases can be identlfied from the simplex tableaus 9 Unbounded Alternate Optimal Infeasible Degenerate Optimal Objective coefftcients for NonBasic varlables are called Reduced Costs Reduced Cost Is the net effect on the Objective Value of Increasing a Non-Basic variable in terms of Cost - Revenue When maximizing, a negative Reduced Cost is a candidate for entering the basis The magnitude of Reduced Cost is the amount of change the Non-Basic variable’s coefficient must undergo so as to become break-even or barely profiiable l l l EM-602 I QM-710 (NJ) Lecture 5’ Page 5-6 Unbounded Problem MAxt= Unbounded 4*,+2x, -x,+IGs2 If at any iteration of the tableaus All constralnt coefficients of non-basic variables...
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