1. Solve the following LPP using simplex method.
Min. \(z=x_{1}-3 x_{2}+2 x_{3}\)
ST \(3 x_{1}-x_{2}+2 x_{3} \leq 7\)
\(-2 x_{1}+4 x_{2} \leq 12\)
\(-4 x_{1}+3 x_{2}+8 x_{3} \leq 10\)
\(x_{1} \geq 0, x_{2} \geq 0, x_{3} \geq 0\)
Problem on Linear programming and Simplex methodThe \(\ell_{1}\) norm of a vector \(v \in \mathbb{R}\) is defined by$$ \|v\|_{1}:=\sum_{i=1}^{n}\left|v_{i}\right| $$Problems of the form Minimize \(\|v\|_{1}\) subject to \(v \in \mathbb{R}^{n}\) and \(A v=b\) arise very frequently in applied math, particularly in the field of compressed sensing.Consider the special case of this problem whith \(n=3\),$$ A=\left(\begin{array}{lll} 1 & 1 & 0 \\ 3 & 0 & 1 \end{array}\right) \quad \text { and } \quad b=\left(\begin{array}{l} 3 \\ 8 \end{array}\right) $$(a) (3...
2. Solve the LPP by the dual simplex method Minimize: z = 3x1 + 2x2 Subject to:: x1 + x2 > 1 4x1 + x2 > 2 -X1 + 2x2 < 6 Xi > 0, i=1,2
samplex Problem1: Solve the following problem using simplex method: Max. z = 2 x1 + x2 – 3x3 + 5x4 S.t. X; + 7x2 + 3x3 + 7x, 46 (1) 3x1 - x2 + x3 + 2x, 38 .(2) 2xy + 3x2 - x3 + x4 S 10 (3) E. Non-neg. x > 0, x2 > 0, X3 > 0,44 20 Problem2: Solve the following problem using big M method: Max. Z = 2x1 + x2 + 3x3 s.t. *+...
3. Use the two-phase simplex method to solve the following LP. Min z = x1 + 2x2 Subject to 3x1 + 4x2 < 12 2x1 - x2 2 2 X1, X2 20
SIMPLEX METHOD Solve the following problem using simplex method LP MODEL Let X1 no. of batches of Bluebottles X2 no. of batches of Cleansweeps Objective: Max Z-10X1+20X2 Subject to: 3X1 4X2 S 3 Plant 1 assembly capacity constraint -X1 2-5 5X1 +6X2 s 18 Z, X1, X2 20 Plant 2 capacity constraint Plant 3 capacity constraint
1. Solve the following LP by the simplex method. Min z = 2x2 – Xı – X3 Subject to *1 + 2x2 + x3 = 12 2x1 + x2 – x3 = 6 -X1 + 3x2 = 9 X1, X2, X3 > 0
Exercise 1. Please use the simplex method to solve the below LP min z=3.r - 12 s.t. 21; +12<8 21 +225 21 - 22 S4 21,220 a) Write the LP in standard form. b) Provide tableaus, BV, NBV, solution, objective value for each iteration of the simplex method. (Hint: the optimal value z=-5).
Exercise 1. Please use the simplex method to solve the below LP min z=3.r - 12 s.t. 21; +12<8 21 +225 21 - 22 S4 21,220 a) Write the LP in standard form. b) Provide tableaus, BV, NBV, solution, objective value for each iteration of the simplex method. (Hint: the optimal value z=-5).
Consider the following linear fractional program (LFP):$$ \begin{array}{ll} \max f\left(x_{1}, x_{2}\right)= & \frac{10 x_{1}+20 x_{2}+10}{3 x_{1}+4 x_{2}+20} \\ \text { s.t. } \quad & x_{1}+3 x_{2} \leq 50 \\ & 3 x_{1}+2 x_{2} \leq 80 \\ & x_{1}, x_{2} \geq 0 \end{array} $$(a) Transform this problem into an equivalent linear program.(b) Use Matlab (or other software) to solve the LP you created in part (a).(c) Use your answer from part (a) to find a solution to the original LFP.(d) Does...
QUESTION) Solve the DP given below using the revised simplex method. Min Z = X1 + 2x2 + 4x3 Öyle ki; 2x1 – 2x2 + x3 = 0 -2x1 + 4x2 + x3 = 8 4x1 + 3x2 – 2x3 = 17 X1, X2, X3 20