QUESTION THREEA) Use the simplex method to solve the following LP problem.Maximize Z = 3x, + 5x, + 4x,subiect to the constraints2x, + 3x, < 82x, + 5x, < 103x, + 2x, + 4x3 S 15B)Find the solution using two-phase methodMinimize Z =x, + 2x, + 3x3 - x4Subject to the constraints5x, + 7x, +4x 57-4x, +7x, + 5x, 2 -23x, + 4x, + 6x, 2 29/,CIWrite the dual ofthe following LP problemMaximize Z = x, + 2x, + 3x3Subject to the constraintsX1 + x2 + x3S 102x, - x2 - x3 < 22x, - 2x, - 3x, S6

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Practical Management Science

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Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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WK Qu. 7-11 A firm has prepared the following binary... A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 35x1 + 25x2 +15x3+ 30x4 s.t. 7x1 + 8x2 +7x3 + 13x4 ≤ 18 [Constraint 1} + x4 ≥ 2 [Constraint 2} X1 + x2 + x3 X1 + X2 ≤ 1 [Constraint 3} X1 + X3 ≥ 1 [Constraint 4) X2=X4 [Constraint 5) 1, if location j is selected xj = 0, otherwise Solve this problem to optimality and answer the following questions: a. Which of the warehouse locations will/will not be selected? Location 1 will Location 2 will Location 3 will Location 4 will be selected not be selected Net present value be selected not be selected b. What is the net present value of the optimal solution? (Round your answer to the nearest whole number.) 50 c. How much of the available capital will be spent (Hint: Constraint 1…
8 Use the simplex method to find the optimal solution to the following LP: max z = 5x1 + x2 s.t. 2x, + x2 5 6 X1 - X2 50 X1, X2 2 )
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Please find and solve the attached optimization Problem
A payoff matrix has to be prepared with three alternative products Α1 , Α2 and Α3 . The respective cost costs of these products are K2, K2.50 and K4 per unit and their sale prices are K3, K4 and K5 per unit respectively. The normal production capacity of the plant for production of each of the products Α1 , Α2 and Α3 is 3,000, 2,000 and 1,000 units respectively. i. Showing all the working clearly, prepare the payoff table if the states of demand are high (S1 ) , moderate (S2 ) and low (S3 ) with respective demand levels of 3,000, 2,000 and 1, 000 units. The stocks unsold will be worth half the cost price for the next period. ii. What is the maximax decision? iii. What is the maximin decision? iv. What is equally likely decision? v. What is the criterion of realism decision? Use α = 0.8 vi. Develop an opportunity loss table and determine the minimax decision.
5. Consider the transportation problem having the following parameter table: Destination 1 Destination 2 Destination 3 Source 1 Source 2 Demand The initial BF solution given by Source 1 Source 2 Demand Vj 3 2.9 3 X11 = 3, X12 = 2, X22= 2, X23 = 2. Interactively apply the transportation simplex method to obtain an optimal solution. The initial transportation simplex tableau is Destination 1 Destination 2 3 2.9 3 3 2.7 2.8 4 2.7 2.8 4 2 2 0 0 0 2 Destination 3 supply 5 0 2 supply 5 4 2 4 Ui For each iteration tableau, clearly mark: U₁, V₁ values, č¡¡ + or negative values, the loop, the entering BV, the leaving BV. At the end of each iteration, also write out clearly what the new BF solution, and the new objection value.
ld by the m to spoilage Ho manufacre d 3-27 Farm Grown Umation. 2:3-24 Today's Electronics specializes in manufacturing modern electronic components. It also builds the equipment that produces the components. Phyl- lis Weinberger, who is responsible for advising the president of Today's Electronics on electronic manu- facturing equipment, has developed the following table concerning a proposed facility: products. Each etables and and sells for the end of cessing daily demand ity that daily the probability is 0.3. Farm Gro PROFIT ($) POOR customer demand Tos than the demand, I STRONG FAIR MARKET MARKET MARKET from a competiton is $16 per case. 550,000 110,000 -310,000 Large facility (a) Draw a decision table (b) What do you recomnen 300,000 129,000 -100,000 Medium-sized facility :3-28 In Problem 3-27m believe the probs Small facility 200,000 100,000 -32,000 to changing conons. ignored, what deon wa No facility (a) Develop an opportunity loss table. (b) What is the minimax regret…
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b) The figure below presents an unbounded feasible region of a five constrained LP problem. 10- |(0, 6) 6. (1, 4) 4 (3, 2) 2+ (9, 0) 8 10 i. Write down in terms of x and y the inequalities that represent these constraints. ii. If the objective function is Z = 0.12x + 0.15y, determine the optimal solution to this problem (show the movement of the isocost line). ii. Identify the binding and non-binding constraints.
A manufacturing company has 4 factories and 3 warehouses. The costs for transporting its products from factories to ware houses, the supply capacity of factories and demands in warehouses are given respectively by 6 4 81 70 170 4 3 2 C = 130 S = D= 200 2 4 7 100 130 1 5 8 200 a. Use minimum cost method to find an initial feasible solution. b. Determine the amount of products to be transported from factories to warehouses to minimize the cost.
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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A) Use the simplex method to solve the following LP problem. Maximize z = 3x, + 5x, + 4x, subiect to the constraints 2x, + 3x, S8 2x, + 5x, S 10 3x, + 2x, + 4x, S 15