3) (15 pts) Consider the following LP formulation: max z = x1 + 2x2 s.t. −...

3) (15 pts) Consider the following LP formulation: max z = x1 + 2x2 s.t. − x1 + x2 ≤ 2 x2 ≤ 3 kx1 + x2 ≤ 2k + 3 x1, x2 ≥ 0 The value of the parameter k ≥ 0 has not been determined yet.

The solution currently being used is x1 = 2, x2 = 3. Use graphical analysis to determine the values of k such that this solution is actually optimal.

Expert Solution

If any quire's please comment below and rate by thumb up.please support me. Thank you!

orchestra answered 1 year ago

Consider the TOYCO model given below: TOYCO Primal: max z=3x1+2x2+5x3 s.t. x1 + 2x2 + x3...

Consider the TOYCO model given below: TOYCO Primal: max z=3x1+2x2+5x3 s.t. x1 + 2x2 + x3 ? 430 (Operation 1) 3x1 + 2x3 ? 460 (Operation 2) x1 + 4x2 ? 420 (Opeartion 3 ) x1, x2, x3 ?0 Optimal tableau is given below: basic x1 x2 x3 x4 x5 x6 solution z 4 0 0 1 2 0 1350 x2 -1/4 1 0 1/2 -1/4 0 100 x3 3/2 0 1 0 1/2 0 230 x6 2 0 0...

(Operation Research II Industrial Engineering) Consider the following LP: Minimize z = x1 + 2x2 Subject...

(Operation Research II Industrial Engineering) Consider the following LP: Minimize z = x1 + 2x2 Subject to x1 + x2 >= 1 -x1 + 2x2 <= 3 x2 <= 5 x1,x2 >= 0 (a) Convert the LP given above to the standard form. Determine all the basic feasible solutions (bfs) of the problem. Give the values of both basic and nonbasic variables in each bfs. (b) Identify the adjacent basic feasible solutions of each extreme point of the feasible region....

Consider the following LP. Use revised simplex formula to answer the questions. Max Z = -x1...

Consider the following LP. Use revised simplex formula to answer the questions. Max Z = -x1 +2x3 +3x4 subject to x1 -x2+2x3 ≥8 4x1 +2x2 +7x3 +9x4 ≥ 30 2x1 +3x3 +7x4 ≤ 20 3x1 +x2 -3x3 +4x4 = 1 x1, x2, x3, x4 ≥ 0 a. Show that the basic feasible solution where x1, x2, x3, and x4 is not a feasible solution to the given LP. b. Show that the basic feasible solution where x1, x3, x4, and...

3. Consider the following linear program: MIN 6x1 + 9x2 ($ cost) s.t. x1 +2x2 ≤8...

3. Consider the following linear program: MIN 6x1 + 9x2 ($ cost) s.t. x1 +2x2 ≤8 10x1 + 7.5x2 ≥ 30 x2 ≥ 2 x1,x2 ≥0 The Management Scientist provided the following solution output: OPTIMAL SOLUTION Objective Function Value = 27.000 Variable Value Reduced Cost X1 1.500 0.000 X2 2.000 0.000 Constraint Slack/Surplus Dual Price 1 2.500 0.000 2 0.000 −0.600 3 0.000 −4.500 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 0.000 6.000 12.000 X2 4.500...

Find the Dual of the following LP max z = 4x1 − x2 + 2x3 x1...

Find the Dual of the following LP max z = 4x1 − x2 + 2x3 x1 + x2 ≤ 5 2x1 + x2 ≤ 7 2x2 + x3 ≥ 6 x1 + x3 = 4 x1 ≥ 0, x2, x3 free

4-Consider the following problem: max − 3x1 + 2x2 − x3 + x4 s.t. 2x1 −...

4-Consider the following problem: max − 3x1 + 2x2 − x3 + x4 s.t. 2x1 − 3x2 − x3 + x4 ≤ 0 − x1 + 2x2 + 2x3 − 3x4 ≤ 1 − x1 + x2 − 4x3 + x4 ≤ 8 x1, x2, x3, x4 ≥ 0 Use the Simplex method to verify that the optimal objective value is unbounded. Make use of the final tableau to construct an unbounded direction..

Consider the following linear program: MAX Z = 25A + 30B s.t. 12A +...

Consider the following linear program: MAX Z = 25A + 30B s.t. 12A + 15B ≤ 300 8A + 7B ≤ 168 10A + 14B ≤ 280 Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z. Show the optimal area.

Consider the following linear program: maximize z = x1 + 4x2 subject to: x1 + 2x2...

Consider the following linear program: maximize z = x1 + 4x2 subject to: x1 + 2x2 <= 13 x1 - x2 <= 8 - x1 + x2 <= 2 -3 <= x1 <= 8 -5 <= x2 <= 4 Starting with x1 and x2 nonbasic at their lower bounds, perform ONE iteration of the Bounded Variables Revised Simplex Method. (Tableau or matrix form is acceptable). Show your work. Clearly identify the entering and leaving variables. After the pivot, identify the...

Consider the following. x1 − 2x2 + 3x3 = 3 −x1 + 3x2 − x3 =...

Consider the following. x1 − 2x2 + 3x3 = 3 −x1 + 3x2 − x3 = 2 2x1 − 5x2 + 5x3 = 3 (a) Write the system of linear equations as a matrix equation, AX = B. x1 x2 x3 = (b) Use Gauss-Jordan elimination on [A B] to solve for the matrix X. X = x1 x2 x3 =

Consider the following linear program: MAX Z = 25A + 30B s.t. 12A + 15B ≤...