primal linear programming model?
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what is the dual equivalent and the final tableau of the given primal linear programming model?
Min Y₀ = 10Y₁ + 8Y₂
s.t.
Y₁ + 2Y₂ ≥ 5
2Y₁ - Y₂ ≥ 12
Y₁ + 3Y₂ ≥ 4
Y₁ ≥ 0, Y₂ is unrestricted
prove or disprove the complementary slackness theorem.
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- 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 to Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds Product 2: x2 ≤ 16 units x1, x2, x3 ≥ 0 a) Are any constraints binding? If so, which one(s)? b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. d) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain. e) If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated? f) If profit per unit on each…An Insurance Company is introducing two new product lines: special risk insuranceand mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit onmortgages. Management wishes to establish sales quotas for the new product lines tomaximize total expected profit. Please see figure for work requirements(a) Formulate a linear programming model for this problem.Ana is a university student with 12 hours available daily, and she wants to distribute her time betweenstudy (x) and leisure (y) activities. She wants to maximize her total enjoyment while fulfilling heruniversity obligations. Ana considers leisure to be twice (2) as enjoyable as studying, but she alsobelieves that she should spend at least twice (2) as much time studying as she does on leisure activities.Additionally, she cannot spend more than five (5) hours a day on leisure activities to ensure that she hasenough time for her university obligations. 1. How much additional enjoyment would Ana get if she had one more hour per dayavailable, so 13 instead of 12 (dual price)?2. Would Ana experience a greater level of enjoyment if she allows herself to have amaximum of six hours per day to leisure activities instead of five, while still fulfilling her universityobligations within the 12 hours available (dual price)?3. What is the allowable increase of the coefficient accompanying leisure…
- What is Optimization? How many methods are there to calculate it? Explain this? 2- What do we mean by function Objective? What do we mean by constraints? 3- Give three practical examples (physical or engineering) of a target function with a constraintConsider the following LP problem: Min 6X+ 18Y; Subject to : 3 X + 9Y <= 47, and X + Y <= 141. Which one of the following is true?: a. Slack for each constraint is zero. b. Optimal Obj. function value is 94 c. X=70.5, Y=70.5 is the only optimal solution. d. Optimal Obj. function value is 0Given 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)?
- 1) How many pounds of shrimp should be brought in four weeks if Atlantic Seafood wants to maximize profit? 2) How many pounds of shrimp should be sold in four weeks if Atlantic Seafood wants to maximize profit? 3) What is the total profit for Atlantic Seafood if they follow the optimal solution?Explain all the steps when implementing the Branch and Bound method for the following optimization problem: Max 15*x1+12*x2+4*x3+2*x4 s.t. 8*x1+5*x2+3*x3+2*x4 <=10 3*x1+2*x3<=4 x1, x2, x3, x4 binaryExplain what is meant by the assumptions of linear programming ?
- Max 30x1 x2 s.t. 2x1 x2 ≤ 4 2x1 2x2 ≤ 6 x1, x2 ≥ 0 (a) Solve graphically and state the optimal solution. (b) Keeping all the other data as is, what per unit profitability should the product, whose current optimal value is zero, have in order that this product enter the optimal solution at a positive level? (c) How many optimal corner solutions exist after making the change described in part (b)? What are they? (d) In the original problem, how much can the right-hand side (RHS) of the second constraint be increased (or decreased) before the optimal solution is changed? (e) Answer part (d) for the RHS of the first constraint. (f) How do you explain the difference between parts (d) and (e)? (g) What will be the impact of adding the constraint 4x1 x2 = 4 to the original model? (h) What is the impact (on the optimal solution) of adding the constraint 3x1 3x2 ≤ 15 to the original model? (i) Fill in the blanks: The difference between parts (g) and (h) is that the original optimal solution…a) What is the optimal solution to this problem? Solve it graphically. b) If a technical breakthrough occurred that raised the profit per unit of X1 to $3, would this affect the optimal solution? c) Instead of an increase in the profit coefficient X1 to $3, suppose that profit was overestimated and should only have been $1.25. Does this change the optimal solution?Briefly discuss what is meant by the assumption of linear programming?