Write the dual maximization problem, and then solve both the primal and dual problems with the...

Write the dual maximization problem, and then solve both the primal and dual problems with the simplex method. (For the dual problem, use x1, x2, and x3 as the variables and f as the function.) Minimize g = 6y1 + 28y2 subject to 2y1 + y2 ≥ 14 y1 + 3y2 ≥ 14 y1 + 4y2 ≥ 17 . primal g = primal y1 = primal y2 = dual f = dual x1 = dual x2 = dual x3 =

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orchestra answered 2 years ago

USING EXCEL!! FOR BOTH PROBLEMS SCREEN SHOTS OF WORK PLEASE 19. Write the following primal problem...

USING EXCEL!! FOR BOTH PROBLEMS SCREEN SHOTS OF WORK PLEASE 19. Write the following primal problem in canonical form, and find its dual. Max 3x1+1x2+5x3+3x4 s.t. 3x1+1x2+2x3 = 30 2x1+1x2+3x3+1x4 >= 15 2x2+3x4<= 25 x1,x2,x3,x4 >= 0 20. Photo Chemicals produces two types of photograph-developing fluids at a cost of $1.00 per gallon. Let x1 = gallons of product 1 x2 = gallons of product 2 Photo Chemicals management requires that at least 30 gallons of product 1 and at...

Prove that if the primal minimisation problem is unbounded then the dual maximisation problem is infeasible.

Find the dual problem for each of the following primal problems. a): min z=6x1+8x2 st: 3x1+x2>=4...

Find the dual problem for each of the following primal problems. a): min z=6x1+8x2 st: 3x1+x2>=4 5x1+2x2>=7 x1,x2>=0 b): max z=8x1+3x2-2x3 st: x1-6x2+x3>=2 5x1+7x2-2x3=-4 x1<=0,x2<=0,x3 unrestricted

A primal maximization problem is given. Maximize f = 60x1 + 30x2 subject to 3x1 +...

A primal maximization problem is given. Maximize f = 60x1 + 30x2 subject to 3x1 + 2x2 ≤ 150 x1 + x2 ≤ 70 . (a) Form the dual minimization problem. (Use y1 and y2 as the variables and g as the function.) Minimize g = subject to ≥ 60 ≥ 30 y1, y2 ≥ 0 . (b) Solve both the primal and dual problems with the simplex method. primal x1 = primal x2 = primal f =...

A primal maximization problem is given. Maximize f = 20x1 + 10x2 subject to 3x1 +...

A primal maximization problem is given. Maximize f = 20x1 + 10x2 subject to 3x1 + 2x2 ≤ 90 x1 + x2 ≤ 40 . (a) Form the dual minimization problem. (Use y1 and y2 as the variables and g as the function.) Minimize g = subject to = (b) Solve both the primal and dual problems with the simplex method. primal x1 = primal x2 = primal f = dual y1 = dual y2 = dual g =

Solve the following linear programming problem. You must use the dual. First write down the dual...

Solve the following linear programming problem. You must use the dual. First write down the dual maximization LP problem, solve that, then state the solution to the original minimization problem. (a) Minimize w = 4y1 + 5y2 + 7y3 Subject to: y1 + y2 + y3 ≥ 18 2y1 + y2 + 2y3 ≥ 20 y1 + 2y2 + 3y3 ≥ 25 y1, y2, y3 ≥ 0 (b) Making use of shadow costs, if the 2nd original constraint changed to...

MINIMIZATION BY THE SIMPLEX METHOD convert each minimization problem into a maximization problem, the dual, and...

MINIMIZATION BY THE SIMPLEX METHOD convert each minimization problem into a maximization problem, the dual, and then solve by the simplex method. 1>. Minimize z = 6x1 + 8x2 subject to 2x1 + 3x2 ≥ 7 4x1 + 5x2 ≥ 9 x1, x2 ≥ 0 2>. Minimize z = 4x1 + 3x2 subject to x1 + x2 ≥ 10 3x1 + 2x2 ≥ 24 x1, x2 ≥ 0

3. Solve the following linear programming problem. You must use the dual. First write down the...

3. Solve the following linear programming problem. You must use the dual. First write down the dual maximization LP problem, solve that, then state the solution to the original minimization problem. (a) Minimize w = 4y1 + 5y2 + 7y3 Subject to: y1 + y2 + y3 ≥ 18 2y1 + y2 + 2y3 ≥ 20 y1 + 2y2 + 3y3 ≥ 25 y1, y2, y3 ≥ 0 (b) Making use of shadow costs, if the 2nd original constraint changed...

QUESTION 1: Solve the linear programming model given below using the simplex method. Write the primal...

QUESTION 1: Solve the linear programming model given below using the simplex method. Write the primal and dual results from the optimal table you obtained. MAX Z = 10?1 + 20?2 + 5?3 6?1 + 7?2 + 12?3 ≥ 560 5?1 − 3?2 + x3 ≤ 100 2000?1 + 1000?2 + 1000?3 ≤ 62298 ?1,?2,?3 ≥ 0 IMPORTANT REMINDER ABOUT THE QUESTION SOLUTION: NEW ORDER CALCULATIONS SHOULD BE WRITTEN DETAILED WHEN CREATING THE SYMPLEX TABLES. WHEN THE CALCULATIONS ARE SHOWED AND...

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...

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