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

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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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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…
3) Maximize Z= 2x, +x2 +3x 3 X+x2+2x3 <25 + X3 5 8 X2+ x3 S10 X1, X2, X3 2 0 Subject to IMe
On the graph on right, the constraints C₁ and C₂ have been plotted. Using the point drawing tool, plot the four corner points for the feasible area. The optimum solution is: X=0.00 (round your response to two decimal places). Y = 4.00 (round your response to two decimal places). Optimal solution value Z = 24.00 (round your response to two decimal places).
The following is a payoff an Electronic Company's Product The State of Nate Decision Alternative 0.69 0.31 S2 D1 14 D2 13 D3 11 The Expected values for the payoff table as follows: E(D1= 5.72 EID2)= 11.45 EID3) 9.14 What should be the payoff value for the D2 under S1 to keep the solution.or Clek Sne and Sub to abeit Cliok Soella e all ao
Scenario You are going to plant a rectangular flower bed consisting of tulips in the middle surrounded by daisies on the outside. You have the same amount of each flower and will need an equal area for each. You want the border of daisies to be uniform around the tulips in the middle, as shown in the diagram below:
The Ace Manufacturing Company has orders for three similar products. Product A Min 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 B B Ic C Product 1 12 3 Orders (units) 1,900 500 1,100 Capacity (units) 1,300 1,600 800 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 (a) Develop the linear programming formulation of this problem. (Let XA1 be the number of units of product A produced by machine 1, X;; be the number of units of product i produced by machine j, etc.)
) The following data have been prepared for master production scheduling purposes in IKEA Australia: End product A: Beginning inventory of 60, Period forecast of 10, Lot size of 30, and 30 hours in lot size. End product B: Beginning inventory of 20, Period forecast of 5, Lot size of 20, and 20 hours in lot size. End product C: Beginning inventory of 30, Period forecast of 15, Lot size of 50, and 50 hours in lot size. Capacity: 38 hours/ week (i) Prepare the master production schedule for these items during the next four periods using the Ethan Allen master production scheduling method. (ii) Suppose that the master production schedule is frozen for the next three periods. What specific impact would the policy have on the IKEA's performance?
A. Solve the following linear program by the solver method. P = 100x + 200y 3x + 3y 2 16 14x + 5y s 10 2x + 7y z 10 x, y 20 4. Maximize: Subject to: Solver Solution: B D E 1 Decision: 4 Constraints: Total Used Sign Available 5 1 6 2 7 3 8 Maximize P: 3.
example 1a 1.plot all the corner points for the feasible area. 2. Find the optimum solution to X= Y= VALUE Z=
1. Consider four bases of operation B, and three targets T, The tons of bombs per aircraft from any base that can be delivered to any target are given in the following table: Target (T;) T2 T3 Base (B;) B2 6 6 B3 10 8 4 B4 8 4 The daily sortie capability of each of the four bases is 150 sorties per day. The daily requirement of sorties spread over each individual target is 200. Find the allocation of sorties from each base to each target which maximizes the total tonnage over all three targets. Explain each step in the process. B,

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