Please solve the problem Sub parts B,C,D thank u... Im very needed in 60-120 minutes max. thank u tor he expert, please solving 1. The city of Busville contains three school districts. The number ofminority and nonminority students in each district is given in Table 1.Of all students, 25% (200/800) are minority students.The local court has decided that both of the town's two high schools(Cooley High and Walt Whitman High) must have approximately thesame percentage of minority students (within + 5%) as the entire town.The distances (in miles) between the school districts and the highschools are given in Table 2. Each high school must have an enrolmentof 300 – 500 students. The city school board needs to determine anassignment of students to schools that minimizes the total distancestudents must travel to schools.Table 1. Number of studentsTable 2. Distances (in miles)Minority NonminorityDistrict StudentsCooleyDistrict High WhitmanWaltStudentsHigh1.502001.82.95025022.81.910015031.81.9(Adapted from Winston 2004)PL = Program Linear or Linear Program ( LP)%3D2.3. A. Formulate the problem into the OT model! Define the decisionvariables clearly. Give information about the objective function andconstraints.B. Find the optimal solution of the PL model! Use the same variablename (consistent) as you used in No. 1. The order of constraintscorresponds to the order of constraints in No.1. Include evidence in theform of PL MODELS AND SOLUTIONSC. Based on the solution obtained in No. 2, write a recommendation forthe City of Busville School Board! Show that your recommendationmeets all the requirements and that all students in the 3 districts get aschool.D. Currently the maximum number of students that can be admitted toWalt Whitman High (call it bwWma) is 500 people. What is theallowable bwwmax value so that the current base remains optimal?Explain with evidence.

B. Find the optimal solution of the PL model! Use the same variable name (consistent) as you used in No. 1. The order of constraints corresponds to the order of constraints in No.1. Include evidence in the form of PL MODELS AND SOLUTIONS C. Based on the solution obtained in No. 2, write a recommendation for the City of Busville School Board! Show that your recommendation meets all the requirements and that all students in the 3 districts get a school. D. Currently the maximum number of students that can be admitted to Walt Whitman High (call it bwwmax) is 500 people. What is the allowable bwwmax value so that the current base remains optimal? Explain with evidence.

B. Find the optimal solution of the PL model! Use the same variable name (consistent) as you used in No. 1. The order of constraints corresponds to the order of constraints in No.1. Include evidence in the form of PL MODELS AND SOLUTIONS C. Based on the solution obtained in No. 2, write a recommendation for the City of Busville School Board! Show that your recommendation meets all the requirements and that all students in the 3 districts get a school. D. Currently the maximum number of students that can be admitted to Walt Whitman High (call it bwwmax) is 500 people. What is the allowable bwwmax value so that the current base remains optimal? Explain with evidence.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 71P

See similar textbooks

Similar questions

The board of directors of General Wheels Company is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table. Investment Opportunity 1 2 3 4 5 6 7 Estimated Profit ($million) 17 10 15 19 7 13 9 Capital Required for Investment Opportunity ($million) Capital Available ($million) 1 2 3 4 5 6 7 Capital 43 28 34 48 17 32 23 100 The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5, 6, and 7. The objective is to select the combination of capital investments that will maximize the total estimated long-run…
2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest. Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%. The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per P40,000 invested. The Diversified fund has a risk rating of 4 per P40,000 invested. For example, if P400,000 is invested in each of the two investment funds, Provident’s risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, Provident developed…
3.Ruth Jones, the marketing manager for a department store chain is trying to decide on the optimal allocation of her advertising budget for the next quarter. Jones has the data that indicate that television commercials and newspaper advertisements have the following impact on sales revenue (R) R = 20,000T + 5000N + 20,000TN - 1O00T2 where T represents the number of commercials on T.V. and N the number of full-page newspaper advertisements. Each T.V. commercial costs $10,000 and each newspaper advertisement costs $5000. The advertising budget is limited to be $100,000. (a)Calculate the optimal amount of advertisement in each medium if the firm is interested in maximizing its sales revenue. Calculate the consequent value of sales revenue. (b)By how much should sales revenue increase if the advertising budget increases by a very small amount? Show and explain your calculations.
The equation below specifies a function with independent variable x. Determine whether the function is linear, constant, or neither x=2y+5
The number of crimes in each of a city’s three policeprecincts depends on the number of patrol cars assigned toeach precinct (see Table 11). Five patrol cars are available.Use dynamic programming to determine how many patrolcars should be assigned to each precinct. No. of Patrol Cars Assigned to PrecinctPrecinct 0 1 2 3 4 51 14 10 7 4 1 02 25 19 16 14 12 113 20 14 11 8 6 5
Simplex Method Solve the following LP problem using the simplex method. Maximize: P = 9x + 7ySubject to:2x + y ≤ 40 x + 3y ≤ 30x, y ≥ 0 What is the entering variable and leaving variable in Table 1? Choices: A. Entering Variable: y and Leaving Variable: S1 B. Entering Variable: x and Leaving Variable: S1 C. Entering Variable: x and Leaving Variable: S2 D. Entering Variable: y and Leaving Variable: S2
The captain of a cricket team has to allot five middle batting positions to five batsmen. The average runs scored by each batsman at these positions are as follows: Batsman Batting position IV V P 40 40 40 35 25 50 Q 42 30 16 25 27 R 50 48 40 60 50 S 20 19 20 18 25 T 58 60 59 55 53 • Batsmen 'U' with the following average runs in batting positions as given below: Batting position IV V Average runs 45 52 38 50 49
Simplex Method Solve the following LP problem using the simplex method. Maximize: P = 9x + 7ySubject to:2x + y ≤ 40x + 3y ≤ 30x, y ≥ 0 What is the entering variable and leaving variable in Table 2? a. Entering Variable: x and Leaving Variable: S2 b. Entering Variable: y and Leaving Variable: S2 c. Entering Variable: y and Leaving Variable: S1 d. Entering Variable: x and Leaving Variable: S1
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 ≥ 0
Globex Investment Capital Corporation owns six companies that have the following estimatedreturns (in millions of dollars) if sold in one of the next 3 years:Year Sold(Estimated return, $1,000,000s)Company 1 2 31 14 18 232 9 11 153 18 23 274 16 21 255 12 16 226 21 23 28To operating funds, the company must sell at least $24 million worth of assets in year 1, $28million in year 2, and $32 million in year 3. Globex wants to develop a plan for selling thesecompanies during the next 3 years to maximize return.(a) Formulate an integer programming model for this problem.
A manufacturing firm has discontinued production of a certain unprofitable product line. Considerable excess production capacity was created as a result. Management is considering devoting this excess capacity to one or more of three products: X1, X2, and X3.Machine hours required per unit are PRODUCT MACHINE TYPE X1 X2 X3 Milling machine 8 2 1 Lathe 4 1 7 Grinder 2 1 3 The available time in machine hours per week is MACHINE HOURS PER WEEK Milling machines 1,000 Lathes 560 Grinders 270 The salespeople estimate they can sell all the units of X1 and X2that can be made. But the sales potential of X3 is 80 units per week maximum.Unit profits for the three products are UNIT PROFITS X1 $ 12 X2 9 X3 13 a. Set up the equations that can be solved to maximize the profit per week. (Leave no cells blank - be certain to enter "0" wherever required.) s.t b. Solve these equations using the Excel Solver. (Leave no cells blank -…
A manufacturing firm has discontinued production of a certain unprofitable product line. Considerable excess production capacity was created as a result. Management is considering devoting this excess capacity to one or more of three products: X1, X2, and X3.Machine hours required per unit are PRODUCT MACHINE TYPE X1 X2 X3 Milling machine 2 3 4 Lathe 6 8 0 Grinder 8 0 2 The available time in machine hours per week is MACHINE HOURS PER WEEK Milling machines 502 Lathes 552 Grinders 180 The salespeople estimate they can sell all the units of X1 and X2 that can be made. But the sales potential of X3 is 80 units per week maximum.Unit profits for the three products are UNIT PROFITS X1 $ 39 X2 31 X3 29 a. Set up the equations that can be solved to maximize the profit per week. (Leave no cells blank - be certain to enter "0" wherever required.) s.t b. Solve these equations (Round your answers to the nearest whole…