need help in both problems, 31 and 33.
need help in both problems, 31 and 33. 0 x0, x2 2 Graphically find all solutions...
Use the simplex algorithm to find all optimal solutions to the following LP. max z=2x1+x2 s.t. 4x1 + 2x2 ≤ 4 −2x1 + x2 ≤ 2 x1 ≥1 x1,x2 ≥0
Find all the basic solutions for the following LP problems using the Gauss– Jordan elimination method. Identify basic feasible solutions and show them on graph paper. Maximize z = 4x1 + 2x2 subject to −2x1 + x2 ≤ 4 x1 + 2x2 ≥ 2 x1, x2 ≥ 0
Question 3: Identify which of LP problems (1)--(4) has (x1,x2) = (20,60) as its optimal solution. (1) min z = 50xı + 100X2 s.t. 7x1 + 2x2 > 28 2x1 + 12x2 > 24 X1, X2 > 0 (2) max z = 3x1 + 2x2 s.t. 2x1 + x2 < 100 X1 + x2 < 80 X1 <40 X1, X2 > 0 (3) min z = 3x1 + 5x2 s.t. 3x1 + 2x2 > 36 3x1 + 5x2 > 45...
Min 2x1 + x2 s.t. x1 + x2 ≥ 4 x1 – x2 ≥ 2 x1 – 2x2 ≥ –1 x1 ≥ 0, x2 ≥ 0 Please solve the linear program graphically, showing the objective function, all constraints, the feasible region and marking all basic solutions (distinguishing the ones that are feasible).
2. (20 pts.) Find the optimal s method lex olution for the following LP problem using the appropriate simp (Hint: DO NOT use the big-M method) Minimize Zx+4x2+ 3x4 xi + 2x2 - xx42 3 -2x124x3x2 S.t. and x1, x2, x3, x20
Problem 2: (This is from Problems 4 and 5. Page 172 of the textbook) (a) Use Phase I Simplex Algorithm to find an initial basic feasible solution. Next, use the Simplex Tableau Method to solve this problem. Show that if ties are broken in favor of lower-numbered rows, then cycling occurs when the Simplex method is used to solve the following LP: max z-3x1 +x2 - 6x3 9x1 x2 -9x3 -2 x40 xi + (1/3)X2 - 2x3 - (1/3)X0 9x1...
Use the Big M method to find the optimal solution to the following LP: min z = -3x1 + x2 s.t. X1 - 2x2 2 -x1 + x2 3 x1, x2 0 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
i) Find all values of a for which all solutions of the differential equation y/ar 2)y = 0, x0 approach zero as x -+ 0. i) Find all values of a for which all solutions of the differential equation y/ar 2)y = 0, x0 approach zero as x -+ 0.
6. Find the solutions of the following initial-value problems: dr (b) xt-=-(X2+12). X( 2 )=-1 dr dr dr (e)- r +2.xi, x() 4 dr
Solve the following linear programming problems as directed. Put in a box the values of all the variables you use in your solution, as well as the optimal value of the objective function. a) SIMPLEX METHOD Max Z = 11X1 + 10X2 s.t. 2 X1 + X2 <= 150 4 X1 + 3 X2 <= 200 X1 + 6 X2 <= 175 X1, X2 >= 0 b) GRAPHIC METHOD (do not forget to indicate the feasible region) Min Z = 30...