5. Consider the following LP problem:Maximize z = 2x1 + 4x2 + 4x3 – 3x4Subject toX1 + x2 + x3 = 4x1 + 4x2 + x4 = 8X1, X2, X3, X4 20Use the dual problem to show that the basic solution (x1, x3) is not optimal solutionto the problem.

The linear programming process is a process through which the value of the variables that maximize…

Answered: 5. Consider the following LP problem:…

Practical Management Science

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Chapter2: Introduction To Spreadsheet Modeling

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Maximize Z = x₁ + x₂, subject to X₁ X₂ ≤-3 2x₁ + 7x₂ ≤ 4 and x₁ ≥ 0, x₂ ≥ 0.
Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 11 4 $B$3 Product_2 175 0 25 12 14 $B$4 Product_3 0 −1.5 25 8 5 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 multiple choice Product_1 Product_2 Product_3
example 5a
Estimate a range for the optimal objective value for the following LPs: *(a) Minimize z = 5x₁ + 2x₂ subject to (b) Maximize z subject to x₁ + 5x₂ + 3x3 X₁ X₂ ≥ 3 2x₁ + 3x₂ = 5 X1, X₂ ≥ 0 x₁ + 2x₂ + x3 = 30 2x₁ - x₂ = 40 X1, X2, X3 ≥ 0
Consider the apportionment of 27 projectors for a school district with four campus locations labeled A, B, C, and D. The following table shows the apportionment of the projectors using the Hamilton method. A B 836 1936 C 312 Campus Enrollment Apportionment of 27 projectors 4 9 1 D 2736 13 (a) If the number of projectors to be apportioned increases from 27 to 28, what will be the apportionment if the Hamilton method is used? Campus A Campus B Campus C Campus D Did the Alabama paradox occur? O Yes O No (b) If the number of projectors to be apportioned using the Hamilton method increases from 28 to 29, will the Alabama paradox occur? O Yes O No
Bugs Bunny and Daffy Duck are contestants on a game show called Split or Steal. On the show, Bugs and Daffy have to pick one of two cards and decide to split the prize money of $100,000 or steal it from the other contestant. The decisions are made simultaneously so neither player knows what the other will do. The table below represents the result of the contestants’ choices. See attached What should a rational player do in this game? Is this a zero-sum game?
1. A specific assignment of values to decision variables is called what? a. Constraint b. Feasible c. Solution d. None of the above 2. Which of the following must be true of a feasible solution a. All of what Solver calls changing variables must be greater than 0 b. It is optimal c. It violates no constraints d. None of the above
FIND THE OPTIMUM SOLUTION TO X= Y= MAX Z=
The image shows the graph of y = |+2| in black and y = 3 in red. Use the graph to solve the inequality |x+2<3. i. On the graph, shade the parts of the x-axis showing where |+2| < 3. 10+ 9 10 -9 -8 -7 -6 -5 -4 -3 -2 Clear All Draw: 1 8 7 6 5 2 4 6 8 9 16 1 -2+ کہ وہ کر: 1 ii. Write the shaded part of the x-axis using interval notation:
Consider the following problem (P): Minimize Z = -5x1 + 4r2 2.13 (1) (2) subject to 12 + 4r3 0. Use the tabular form of the simplex method to determine an optimal solution for (x1, x2, X3) and the associated optimal value for Z. In each simplex tabular, identify the current basic solution, the corresponding solution for (r1, r2, T3), and the associated value for Z. Define all variables clearly.
1. Write a linear program for the problem. 2. What is the optimal production mix among different coffee varieties and the profit associated with it? 3. What should be the per bag profit of Tarrazu which will make it beneficial to produce this variety? 4. One Cup is considering increasing the weekly bags to 150. If it costs One Cup $3.00 per bag to procure beans of any variety. Conduct sensitivity analysis and determine if One Cup should consider increasing the per week production. 5. Identify the range over which per bag profit of Sumatra and Kona may vary and still retain the current production plan as optimal for One Cup. 6. Once roasted the coffee beans must be preserved properly. To ensure that, One Cup Coffee is considering investing in a vacuum packaging machine for 24 hours/ week. It takes 10, 15 and 10 minutes to pack a bag of Sumatra, Kona and Tarazzu respectively. Identify if the current production plan will suit the installation of the new packaging scheme.
Variable Cells Model Variable Constraints E S D Constraint Number 1 E 2 3 S D S D Name Economy Models Standard Models Deluxe Models Name Total Profit: $ Fan Motors Cooling Coils Manufacturing Time Optimal Solution Constraints Fan motors Cooling coils Final Value 80.000 120.000 0.000 Final Value 200.000 320.000 2080.000 a. Identify the range of optimality for each objective function coefficient. If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place. Objective Coefficient Range Variable lower limit upper limit E Reduced Cost 0.000 0.000 -24.000 Manufacturing time. AUTO Shadow Price 31.000 32.000 0.000 Right-Hand-Side-Range lower limit upper limit Objective Coefficient 63.000 95.000 135.000 b. Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal…

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5. Consider the following LP problem: Maximize z = 2x1 + 4x2 + 4x3 - 3x4 Subject to X1 + x2 + x3 = 4 X1 + 4x2 + x4 = 8 X1, X2, X3, X4 N0 Use the dual problem to show that the basic solution (x1, x3) is not optimal solution to the problem.