Solve by the Big M – method: Maximize Ζ= x1 + 2x2 −3x3 + x4 Subject to x1 +2x2 +3x3 =15 2x1 +x2 + 5x3 = 20 x1 +2x2 +x3 +x4 = 10 x1 + 4x2 +6x3 ≤ 5 Where x x x x1, 2, 3, 4 ≥ 0
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- Solve by the Big M – method:
Maximize Ζ= x1 + 2x2 −3x3 + x4 Subject to x1 +2x2 +3x3 =15
2x1 +x2 + 5x3 = 20
x1 +2x2 +x3 +x4 = 10
x1 + 4x2 +6x3 ≤ 5
Where x x x x1, 2, 3, 4 ≥ 0
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- This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.Use the simplex method to solve. Maximize z = 4x1 + 2x2, subject to 3x1 + x2 < 22 3x1 + 4x2 < 34 x1 > 0, x2 > 0 x1 = x2 = x3 =Use the graphical method to solve the following problem: max Z = 2x1 + x2 subject to: 3x1 + x2 ≤ 44 2x1 + 5x2 ≥ 60 x1 + x2 ≤ 18 x2 ≤ 10 x1, x2 ≥ 0
- Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2x1 - x2 ≤ 2 3x1 - 4x2 ≤ 8 x1, x2 ≥ 0b) Maximize z = 3x1 + 2x2 Subject to: 4x1 - x2 ≤ 8 4x1 + 3x2 ≤ 12 4x1 + x2 ≤ 8 x1, x2 ≥ 0Solve Maximize: Z = 4X1 + 3X2 + 9X3 Subject to: 2X1 + 4X2 + 6X3 ≥ 15 6X1 + X2 + 6X3 ≥ 12 X1, X2, X3 ≥ 0 Use simplex method.Solve the following problem with Excel Solver:Maximize Z = 3X + Y.1 2X + 14Y ≤ 85 3 X + 2Y ≤ 18Y≤ 4
- Consider a small Oil production firm with 5 competing oil production projects, A - E. The table below shows the estimated long-term profit (Net Present Value) for each project as well as the amount of investment capital required to start the project. You have been contacted to help select the best combination of projects to maximize the Net Present Value subject to the capital investment limit of $32 million. Production Project A B C D E Estimated Profit (millions) 25 20 19 28 21 Capital Required (millions) 11 8 14 19 13 Formulate a Binary Integer Programming (BIP) model on a spreadsheet. Solver the model using Solver.a. Maximize Z = 6X1 + 18X2+20X3 (Don't use excel shortcut solve manually by Simplex LPP method)Sub toX1 + X2 +X3 = 6010X1 +15X2 +20X3 = 9002X1 + 3X2 +3X3≤100And X1, X2, X3 >=0Given the following LP: Min 4x1 + 6x2 s.t 2x1 + 2x2 ≥ 3, x1 + 3x2 ≥ 2, x1 + 3x2 ≥ 0, Find its dual LP. Use graphical method or the Simplex algorithm, solve the primal LP in (1). Use graphical method or the Simplex algorithm, solve the dual LP (that you find in Part A). Find its dual LP.
- b) Maximize Z = −40X1 −100X2s.t 10X1 + 5X2 ≤ 2502X1 + 5X2 ≤ 1002X1 + 3X2 ≤ 90X1, X2 ≥ 0Solve by simplex method, what are the solutions? Show that this problem hasmultiple solutions and find the solutions?Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. Maximize f = 8x + 9y + 3z subject to 2x + 7y + 8z ≤ 100 6x + 3y + z ≤ 160 3x + 4y + 9z ≤ 10 .Solve the following problem after finding its dual. Min z = x1 - 3x2 + 3x3 s.t. 3x1 - x2 + 2 x3 ≤ 7 2x1 + 4x2 ≥ -12 -4x1 + 3x2 + 8x3 ≤ 10 x1, x2, x3 ≥ 0