Four qualified postgraduate students are to be allocated to four professors. The preferencegiven by student (scale 1-10) is shown as table below.StudentAВCDProfessorJamesJordanJanet786.Jessy58.7(a) Formulate a linear programming model for the problem.[NOTE: Please use x,where i = 1, 2,...,n -Professor and j=1, 2,...,m -Student torepresent your decision variables.](b) From the output below, what is the optimal allocation plan and what is the totalpreference scales obtained from the allocation plan?Model Variable Original ValueFinal ValueValue x1111Value x121Value x131Value x14Value x21Value x22Value x2311111Value x241Value x31Value x32Value x331111Value x341Value x411Value x421Value x431Value x4411699445

Answered: Image /qna-images/answer/1f2eae63-2067-493f-a50f-79ad0767a3b1.jpg

Answered: Four qualified postgraduate students…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

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

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1. Given the LP model below. Do the following: a. Formulate the new LP model. b. Set up the initial table then identify the optimum column, pivotal row, entering variable out, going variable, Zj row entries, and Cj n-Zj row entries Maximize eamings = $0.80xX₁ + $0.40X₂ + $1.20X3 - $0.10X4 subject to X₁ + 2X₂ + X3 + 5X₁150 X₂ 4X₂ + 8X₂ = 70 6X₁ + 7X₂ + 2X3 - X₂ 120 X₁, X₂, X₁, X₁Z 0
Part I. On Simplex Method Given: Min C = 3X1 + 7X2 + 5X3 Subject to: Х1 + X2 + Xз > 50 2X1 + 3X2 + Xз> 100 X1, X2, X3 2 0
find the a. decision variables b. objective function c. constraints
The Ace Manufacturing Company has orders for three similar products. Product Min A s.t. B C 1 2 Machine 3 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A A LB B Ic C Product 4 2 3 Orders (units) Machine 1 Capacity Product A Orders Machine 2 Capacity Product B Orders Machine 3 Capacity Product C Orders 1,800 X20 for all i, j. 700 1,100 Capacity (units) 1,400 (a) Develop the linear programming formulation of this problem. (Let x₁ be the number of units of product A produced by XA1 machine 1, x,, be the number of units of product i produced by machine j, etc.) 1,500 1,000 1 Machine $1.00 $1.30 $1.10 2 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 3 (b) Solve the transportation model for the…
33 White & Becker Tools (W&B) requires 2,000 elec- tric motors next month for its product line of weed trimmers. Each motor is composed of three com- ponents: a coil, a shaft, and housing. W&B has the capability to produce these components or purchase them from an outside vendor. The costs of produc- ing them and purchasing them are shown in the following table. COMPONENT Coil Shaft Housing DEPART- MENT PRODUCTION COST PER UNIT Fabrication 0.5 Molding 0.4 Inspection 0.2 $2.60 $1.80 $1.40 The components that are produced by W&B must pass through three departments: fabrication, molding, and inspection. The number of hours each component requires in each department and the total number of hours available next month in each department are shown in the following table: 0.2 0.7 0.3 PURCHASE COST PER UNIT COIL SHAFT HOUSING AVAILABILITY (HR.) (HR.) (HR.) (HR.) $3.12 $2.16 $1.68 0.6 0.3 0.4 3,000 3,000 1,800 In order to determine the number of components that will be produced and the number…
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allons of deionized water from each wholesaler to each distribution center is shown in the following table: Question Viewer a. Which of the following statements regarding setting up the tableau for the optimal solution for this problem is true? B. The sum of supply capacities is greater than the sum of demands, so a dummy distribution center is needed. C. The sum of supply capacities is less than the sum of demands, so a dummy wholesaler is needed. b. What is the total cost of the solution? The optimal cost is $ ((Enter your response rounded to the nearest dollar.)
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