Solve the following M_Technique. Max Z= 2x1 +3x2-4x3 Subject to x1+x2+x3=8 2x1-5x2+x3=10 x1,x2,x3>=0
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- Max Z = 3X1 + 4X2 Sub to: X1 + X2 ≤ 20 2X1 + 3X2 ≤ 50 And X1, X2 ≥ 0 (SOLVE MANUALLY USING SIMPLEX METHOD PLEASE DON'T USE SHORTCUTS)Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.WHAT IS THE NEW TOTAL VALUE? A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2), and chips (x3). The process requires pine bark, machine time, labor time, and storage space. The following model has been developed. Maximize 9x1 + 9x2+ 6x3 (profit) Subject to Bark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutes Labor 2x1 + 4x2 + 3x3 ≤ 480 hours Storage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 What is the new value of the objective function, if the profit on chips increases from $6 per bag to $7 per bag? The New Value Is=
- A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2), and chips (x3). The process requires pine bark, machine time, labor time, and storage space. The following model has been developed. Maximize 9x1 + 9x2+ 6x3 (profit) Subject to Bark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutes Labor 2x1 + 4x2 + 3x3 ≤ 480 hours Storage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 a-1. What is the marginal value of a pound of pine bark? a-2. Over what range is this price value appropriate? b. What is the maximum price the store would be justified in paying for additional pine bark? c-1. What is the marginal value of labor? c-2. Over what range is this value in effect? d. If the manager could add an additional 60 minutes of labor, should she? Yes or No e. If the manager can obtain either additional pine bark or additional storage space, which one should she choose and how much (assuming additional…Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 17x + 19y subject to 8x + 14y ≥ 21 11x + 6y ≥ 31 and x ≥ 0, y ≥ 0. What is the optimal value of x and y? What is the minimum value of the objective function? Please show me step by step how to do this by hand, not through excel.) Use excel to solve the following linear program. Max. 4X + 5Y s.t 10X + 2Y ≤ 30 3X + 2Y ≤ 12 2X + 2Y ≤ 10 X,Y ≥ 0 a) What is the optimal solution? Give values for all variables. b) What is the objective function value for the optimal solution? c) Submit your excel workbook
- Although the problems say solve graphically, please solve all problems using the QM for Windows software or solve manually. B.6 The Christina Alvarez Company manufactures two lines of designer yard gates, called model A and model B. Every gate requires blending a certain amount of steel and zinc, the company has available a total of 25.000 Ib of steel and 6,000 lb of zinc. Each model A gate requires a mixture of 125 Ib of steel and 20 lb of zinc, and each yields a profit of 590. Each model B gate requires 100 1b of steel and 30 ib of zinc and can be sold for a profit of $70. Find by graphical IP the best production mix of yard gates.Consider the following linear programming (LP) problem: Given f(x1, x2) = 2x1 + 4x2, min f(x1, x2) subject to 2x1 + x2 ≥ 2 x1 ≥ 0 x2 ≥ 0 Solve the problem by the simplex method. Check the optimality of your solution by drawing a figure. (Hint: Look at the example in the lecture note 9. The simplex method has two phases. )Given this linear programming model, solve the model and then answer the questions that follow.Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.Subject toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?
- A Garment Company manufactures blue jeans. Three designs are considered: A, B, and C. The manufacture of design A requires 5 minutes machine time, 20 minutes labor and costs P325. Design B requires 8 minutes machine time, 30 minutes labor and costs P350 to produce. Finally, design C, the top of the line requires 10 minutes machine time, 1 labor hour, and costs P425 to produce. Brand A sells for P650, brand B for P750, and brand C for P875. The company works on a weekly schedule of five days, with two shifts of 7.5 hours (net time) each. It has six machines available for production and 36 workers on each shift. Its weekly manufacturing budget is P1,750,000. Based on previous demand, they can sell at least 500 units of design B and minimum of 200 units of brand C. Formulate the complete LP model.Solve the following problem with Excel Solver:Maximize Z = 3X + Y.1 2X + 14Y ≤ 85 3 X + 2Y ≤ 18Y≤ 4