Find the optimum solution to the following LP using the Simplex Algorithm. Use Two-Phase method. ???...

Find the optimum solution to the following LP using the Simplex Algorithm. Use Two-Phase method.

??? ?=3?2+2?3 ??
−2?1 + ?2 − ?3 ≤ −3

−?1 + 2?2 + ?3 = 6

?1,?2,?3 ≥0

Expert Solution

Colby Messinger answered 1 year ago

Find the optimum solution to the following LP by using the Simplex Algorithm. Min z =...

Find the optimum solution to the following LP by using the Simplex Algorithm. Min z = 3x1 – 2x2+ 3x3 s.t. -x1 + 3x2 ≤ 3 x1 + 2x2 ≤ 6 x1, x2, x3≥ 0 a) Convert the LP into a maximization problem in standard form. b) Construct the initial tableau and find a bfs. c) Apply the Simplex Algorithm.

Using the simplex method, find the optimal solution to the following LP: A company manufactures three...

Using the simplex method, find the optimal solution to the following LP: A company manufactures three products, A,B, and C. The sales volume for A is at least 50% of the total sales of all three products. However, the company cannot sell more than 75 units of A per day. The three products use one raw material, of which the maximum daily availability is 240 pounds. The usage rates of the raw material are 2 lb per unit of A,...

Use the Simplex method to solve the following LP minimize −2x1 −3x2 + x3 + 12x4...

Use the Simplex method to solve the following LP minimize −2x1 −3x2 + x3 + 12x4 subject to −2x1 −9x2 + x3+ 9x4 + x5 = 0 1/3x1 + x2 −1/3x3 −2x4 + x6 = 0 x1,x2,x3,x4,x5,x6 ≥ 0

Solve the following LP using revised simplex algorithm in table format. Min 6x1+10x2 -18x3 +25x4 +15x5...

Solve the following LP using revised simplex algorithm in table format. Min 6x1+10x2 -18x3 +25x4 +15x5 subject to 0.2x1+ 0.2x2+0.4x3+ 0.5x4 + x5 ≥ 1000 2.5x1+ 1.5x2+ x3 + 0.5x4 + 0.5x5 ≤ 1100 0.8x3 + x5 ≥ 500 x1, x2, x3, x4, x5 ≥ 0

Maximization by the simplex method Solve the following linear programming problems using the simplex method. 1>....

Maximization by the simplex method Solve the following linear programming problems using the simplex method. 1>. Maximize z = x1 + 2x2 + 3x3 subject to x1 + x2 + x3 ≤ 12 2x1 + x2 + 3x3 ≤ 18 x1, x2, x3 ≥ 0 2>. A farmer has 100 acres of land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital, and each acre of corn...

Use the simplex method to solve the following problem. Find y1 ≥ 0, y2 ≥ 0,...

Use the simplex method to solve the following problem. Find y1 ≥ 0, y2 ≥ 0, and y3 ≥ 0 such that 2 y1 + 7 y2 + 3 y3 ≤ 11, 2 y1 + 14 y2 + 8 y3 ≥ 1010, and w = 12 y1 + 42 y2 + 59 y3 is minimized. The minimum value w = ___ occurs when y1 = ___, y2 = ___, and y3 = ___. (Simplify your answers.)

Solve the following problem using the simplex method. If the problem is two dimensional, graph the...

Solve the following problem using the simplex method. If the problem is two dimensional, graph the feasible region, and outline the progress of the algorithm. Max Z = 5X1 + 3X2 + 2X3 Subject to 4X1 + 5X2 + 2X3 + X4≤ 20 3X1 + 4X2 - X3 + X4≤ 30 X1, X2, X3, X4 ≥ 0

Identify the type of optimal solution for the following LP problems by the graphical solution method....

Identify the type of optimal solution for the following LP problems by the graphical solution method. Show your work (1) Min 2X1 + 3X2 S.T. 2X1 - 2X2 <= 2 -2X1 + X2 <= 1 X1 => 0, X2 => 0 If the objective function of the above formulation is changed from Min 2X1 + 3X2 to Max 2X1 + 3X2, what type of optimal solution does this problem provide? Note that all constraints remain...

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...

Design a LP FIR filter to meet the following specifications using the window method. Use a...

Design a LP FIR filter to meet the following specifications using the window method. Use a Blackman window. Fs = 25 kHz Fc = 5.0 kHz (3 dB down) Attenuation = 80 dB at 7 kHz Give all the relevant plots (impulse, frequency responses) and the performance of the final filter. Compare this filter to one designed using the optimal method .

Question