Find the optimum solution for the following Integer Linear Programming problem using the CuttingPlane Method.Maximum Profit, z = 7x, + 5x2Subject to:3x, + 4x2 S 256x, + 4x2 s 29X1, X2 20The optimal linear programming tableau is shown in Table 2.Table/Jadual 2Basic VariableCoeficient of /Solution /Pembolehubah Koefisien bagiAsasPenyelesaianX1 X2 S1$21/6 1 42 35 121/2 -1/4 5 41X21X11|-1/3 1/3 1 3

Throughout mathematical optimization, this same cutting-plane approach is any of a range of…

Answered: Find the optimum solution for the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section7.5: Facility Location Models

Problem 25P

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3. The Captain of a Cricket team has to allot 5 middle position to 5 batsmen. The average runs scored by each batsman at these positions are as follows Batting Positions III Batsmen II IV V P 40 40 35 25 50 27 50 42 30 16 25 R. 50 48 40 60 20 19 20 18 25 T 58 60 59 55 Find the assignment of batsmen to positions, which would give the maximum number of runs. If another batsman 'U' with the following average runs in batting positions as given below: Batting Positions: Average Runs: Is added to the team, should he be added to play in the team? If so, who should be replaced by him? II II IV V 45 52 38 50 49
Four qualified postgraduate students are to be allocated to four professors. The preference given by student (scale 1-10) is shown as table below. Student A В C D Professor James Jordan Janet 7 8 6. Jessy 5 8. 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 to represent your decision variables.] (b) From the output below, what is the optimal allocation plan and what is the total preference scales obtained from the allocation plan? Model Variable Original Value Final Value Value x11 1 1 Value x12 1 Value x13 1 Value x14 Value x21 Value x22 Value x23 1 1 1 1 1 Value x24 1 Value x31 Value x32 Value x33 1 1 1 1 Value x34 1 Value x41 1 Value x42 1 Value x43 1 Value x44 1 1 699 445
Variable Cells Model Variable W M Constraints Constraint Number 1 2 3 Name Westem Foods Salsa Mexico City Salsa Name Whole tomatoes Tomato sauce Tomato paste Final Value 560.000 240.000 Reduced Objective Cost Coefficient 0.000 1.000 0.000 1.250 Shadow Price Final Value 4480,000 1920,000 1600,000 0.188 0.125 0,000 Constraint R.H. Side 4480.000 2080.000 1600,000 Allowable Increase 0.250 0.150 Allowable Increase 1120.000 1E+30 40,000 Allowable Decrease 0.107 0.250 Allowable Decrease 160.000 160,000 320.000 Analyze the sensitivity report shown above- a. What is the optimal solution and what are the optimal production quantities? b. Specify the objective coefficient ranges. c. What are the shadow prices for each constraint? Interpret each. d. Identify each of the right-hand-side ranges
3 II | Here are the changes to the original problem and the revised conditions for this decision-making problem: With a favorable market, John Thompson thinks a large facility would result in a net profit of $195,000 to his firm. If the market is unfavorable, the construction of a large facility would result in $185,000 net loss. A small plant would result in a net profit of $110,000 in a favorable market, but a net loss of $25,000 would occur if the market was unfavorable. Doing nothing would result in $0 profit in either market conditions. a) Create a decision table, b) What is your recommendation if you would apply the Maximax criterion (Optimistic)? Follow the guidance from your textbook and create a table. c) What is your recommendation if you would apply the Maximin Criterion (Pessimistic)? Follow the guidance from your textbook and create a table. d) What is your recommendation if you would apply the Criterion of Realism (Hurwicz Criterion) with a coefficient of realism a =…
1. Problem 13-14 (Algorithmic)The following profit payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:State of NatureDecision Alternative S1 S2 S3d1 200 150 75d2 250 150 50The probabilities for the states of nature are P(s1) = 0.5, P(s2) = 0.3 and P(s3) = 0.2.a. What is the optimal decision strategy if perfect information was available? S1 : d2 S2 : d1 or d2 S3 : d1 b. c. What is the expected value for the decision strategy developed in part (a)? If required, round your answer to one decimal place. d. Using the expected value approach, what is the recommended decision without perfect information? d2 What is its expected value? If required, round your answer to one decimal place. e. What is the expected value of perfect information? If required, round your answer to one decimal place.
Using the grid technique to determine the least-cost location (warehouse) for this problem: Tons Rate X - Coordinates Y – Coordinates S1 200 0.5 2 14 S2 300 0.6 6 10 M1 100 1 2 2 M2 100 2 10 14 M3 100 1 14 18 M4 100 2 14 6 The Grid center coordination is ____ and _____ (round the results to 1 decimal place) Group of answer choices (9.9; 7.8) (5.5; 6.9) (8.7; 10.5) (10.5; 6.4) (9.9; 8.9)
3. Consider the transportation problem having the following parameter table: Source Demand Source 1 Source 2 650 Source 3 400 1 2 3 Destination 1 Destination 2 500 750 Demand 10 Vj Assume we have obtained an initial BF solution from northwest corner method, it is: X11 = 10, X12 = 2, X22 = 8, X23 = 9, So the initial transportation simplex tableau looks like below. (Boxed values are cost values, X33 = 1, X34 = 10 circled values are basic variable values.) V₁ = Destination 2 750 800 700 10 1 500 650 400 10 10 800 700 10 ܠ ܕܐ 2 3 300 400 500 10 8 400 500 Destination 3 Destination 4 300 450 10 4 450 600 550 10 9 1 600 Supply 12 550 10 V₁ = 17 11 (10 Supply 12 17 11 Ui U₁² 0 = U₂ = Uz = Do the optimality test (by finding out all u₁, v₁, and čij values, fill all these values in the above table) to determine if the current solution is optimal or not.
26. XYZ and Co has provided the following data seeking your advice on optimum investment strategy: Net return data (in paise) Investment made at the of selected investments Amount beginning of year available (Lakh) 1 95 80 70 60 70 2 75 65 60 50 40 3 70 45 50 40 90 60 40 40 30 30 Маximum Investment (Lakh) 40 50 60 60 The following additional information is also provided: (i) P, Q, R and S represent the selected investments. (ii) The company has decided to have four-year investment plan. (iii) The policy of the company is that amount invested in any year will remain so until the end of the fourth year. (iv) The values (paise) in the table represent net return on investment of 7 1 till the end of the planning horizon (for example, a rupee invested in investment P at the beginning of first year will grow to { 1.95 by the end of the fourth year, yielding a return of 95 paise). Using the above, determine the optimum investment strategy. (CA, November, 1996)
Please show how to solve b
Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimality
6. Find the formulation for the coffee demand in Dubai. 7. Find the constraints will ensure that if Roaster A is selected then Roaster E cannot be selected.
Define Linear programming (LP)?

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Find the optimum solution for the following Integer Linear Programming problem using the Cutting Plane Method. Maximum Profit, z = 7x, + 5x2 Subject to: 3x, + 4x2 25 6x, + 4x2 s 29 X1, X2 20