SYSC3200midterm.docx

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Department
Systems and Computer Engineering
Course
SYSC 3200
Professor
m.ahmed
Semester
Fall

Description
Simplex Tableau 0) Put objective function and constraint equations in table format Objective Function: Z = 4I1 + 6I2, MAX: Z – 4I1 -6I2 = 0 for minimization problems, multiply by -1 and solve like a maximization problem MAX: -Z + 4I1 + 6I2 = 0 Constraints: 0.5 I1 + 0.25 I2 ≤ 4(each 10 oz bottle should contain at most 4 oz of guafenesin) 0.5 I1 + 0.25 I2 + S1 = 4 I1 + 3 I2 ≥ 20 (each 10 oz bottle should contain at least 20 mg of pseudoephedrine HCL) I1 + 3 I2 – S2 + A1 = 20 I1 + I2 = 10 (the mixture of ingredients I1 and I2 make up each 10 oz bottle) I1 + I2 + A2 = 10 W = sum of artificial variables (a1 + a2 + … + an) MIN W = A1 + A2 MIN W –A1 – A2 = 0 MAX –W + A1 + A2 = 0 if RHS is negative, multiply by -1 and treat normally Basic W Z I1 I2 S1 S2 A1 A2 RHS MRT Variable W -1 0 0 0 0 0 1 1 0 never Z 0 -1 4 6 0 0 0 0 0 never S1 0 0 0.5 0.25 1 0 0 0 4 A1 0 0 1 3 0 -1 1 0 20 A2 0 0 1 1 0 0 0 1 10 to put tableau into proper format, get rid of coefficients of artificial variables for W. To do this, subtract each row containing an artificial variable from the phase 1 objective function (W) row. 1 (Phase 1) – goal is to reduce the sum of the constraint violations (RHS in W row) to 0. - choose most negative coefficient in W row, and that’s the pivot element - choose leaving variable with MRT - steps are the same as below, except goal is to make RHS value for W row = 0 - once W = 0, then discard W row, W column, and all artificial variables from tableau, and solve tableau normally for Z 1) Check whether current tableau is optimal 1 a. check objective function row for any negative coefficients; if yes, then solution isn’t optimal => go to step 2) b. if minimization problem, then check for positive coefficients 2) Select entering basic (non-0) variable a. pick the variable with the largest negative coefficient in the objective function row, its column becomes the pivot column. If there’s a tie, choose arbitrarily. 3) Select the leaving variable using MRT a. divide RHS number
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