Stylo Beb Sdn. Bhd. needs to schedule 2 of their designers (Harry & Ryan) onto their next 3 projects(A, B & C). Harry and Ryan each have 80 hours to split between the projects. The following tableshows each designer's capability score for each project, along with the minimum number of hours re-quired for each project:Project A Project B Project CHarry857015Ryan656560Hours Required552575Help Stylo Beb by formulating a Linear Program that maximises total capability.

A linear function that is subject to linear restrictions is what is meant by the term "linear…

Answered: Help Stylo Beb by formulating a Linear…

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 53P

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CSL is a chain of computer service stores. The number of hours of skilled repair time thatCSL requires during the next five months is as follows:Month 1 (January): 6,000 hoursMonth 2 (February): 7,000 hoursMonth 3 (March): 8,000 hoursMonth 4 (April): 9,500 hoursMonth 5 (May): 11,000 hoursEXAMPLE 1 6 Multiperiod Work Scheduling110 CHAPTER 3 Introduction to Linear ProgrammingAt the beginning of January, 50 skilled technicians work for CSL. Each skilled techniciancan work up to 160 hours per month. To meet future demands, new technicians must betrained. It takes one month to train a new technician. During the month of training, atrainee must be supervised for 50 hours by an experienced technician. Each experiencedtechnician is paid $2,000 a month (even if he or she does not work the full 160 hours).During the month of training, a trainee is paid $1,000 a month. At the end of each month,5% of CSL’s experienced technicians quit to join Plum Computers. Formulate an LPwhose solution will…
You work at McKinsey Company and you are in charge of assigning 6 new consultant analysts to projects. There are 5 projects in total. For a given project, up to 3 new consultants can be assigned (i.e., either 0,1,2 or 3 consultants will be assigned to each project). Each consultant is assigned to exactly one project. The table below indicates on which projects the new consultants can be assigned based on their skills and areas of expertise. Project A Project B Project C Project D Project E Consultant 1 Yes Yes Yes No Yes Consultant 2 No Yes No No Yes Consultant 3 Yes No No Yes Yes Consultant 4 Yes Yes Yes Yes No Consultant 5 Yes…
The Kandy Company wants to schedule the following seven-job problem to be processed on two machines A and B. Each job must be processed by two machines A and B, first on machine A and then machine B. The operation processing times at machine A and Bare as follows: Job i 1 2 3 4 5 6 7 Processing time on Machine A (ai) 9 8 7 12 6 8 15 Processing time on Machine B (bi) 6 5 7 19 12 11 7 a. Suppose jobs arrived in their natural order (i.e., job l before job 2, etc.), and FIFO systems of scheduling and processing the jobs is used. What is the completion time of each job and what is the total throughput time (makespan) of all jobs? b. Suppose the inter-arrival times between jobs can be treated as zero and Johnson’s rule is used to sequence and process the jobs, what is the time of each job and what is the total throughput time (makespan) of all jobs? c. What would be the difference in the average time a job spends in the shop…
Company XYZ is contemplating a product development program encompassing 6 major projects. The company is constrained from embarking on all of the projects at once by the number of available (budgeted) developers (60) and the budget allocated for project expenses (£200,000). The following table shows the resource requirements and the estimated profit for each project. Use EXCEL’s Solver to answer questions (1), (2) and (3) in the EXCEL spreadsheets. 1. suppose that project 4 and project 5 are “must-take” projects. What is the revised project portfolio and the revised maximum profit?
A large business process outsourcing company operates 5 days a week (Monday to Friday). The manager estimates that the minimum number of agents requires, a combined on-site and work-from-home (WFH) setup, to provide prompt service: 20 for Monday, 18 for Tuesday, 23 for Wednesday, 28 for Thursday, and 32 for Friday. Labor rules state that each agent must work for 3 days a week on-site. and 2 days in WFH setup. For example. an agent who works on-site Monday to Wednesday must be on WFH setup during Thursday and Friday. Also. the company wants at least 60% of the workforce daily to report on-site. Formulate the appropriate LP model for this problem to minimize the number of agents to be hired.
Finco has the following investments available:Investment A For each dollar invested at time 0, we receive $0.10 at time 1 and $1.30 at time 2. (Time 0 =now;time= 1 one year from now; and so on.)Investment B For each dollar invested at time 1, we receive $1.60 at time 2.Investment C For each dollar invested at time 2, we receive $1.20 at time 3.At any time, leftover cash may be invested in T-bills, whichpay 10% per year. At time 0, we have $100. At most, $50can be invested in each of investments A, B, and C. Formulate an LP that can be used to maximize Finco’s cash onhand at time 3.
An Insurance Company is introducing two new product lines: special risk insuranceand mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit onmortgages. Management wishes to establish sales quotas for the new product lines tomaximize total expected profit. Please see figure for work requirements(a) Formulate a linear programming model for this problem.
Instruction: Formulate the dual problems for X2 the following linear programming model No need to compute/doing a tableau 1. Maximize Z = 2X1 + X2 Subject to: X2 < 10 2X1 + 5X2 < 60 X1 + X2 <18 3X1 + X2 < 44 2. Maximize Z = 2X1 + X2 +3X3 Subject X1 + X2 + 2X3 < 400 2X1 + X2 + X3 < 500 3. Maximize Z = 80X1 + 60X2 Subject X1 + X2 = 200 X1 < 50 X2 > 80
What is true about the assignment problem if the solution has reached the table below? Project A Project B Project C Project D Expert W 0 100 200 0 Expert X 0 0 200 300 Expert Y 0 100 300 0 Expert Z 200 100 0 0 a. The minimum number of vertical and horizontal lines needed to cross out 0s is three. b. Optimal assignment of projects cannot be determined yet. c. Optimal assignment of projects can now be determined.
Company Z is contemplating a product development program encompassing 6 major projects. The company is constrained from embarking on all of the projects at once by the number of available (budgeted) developers (60) and the budget allocated for project expenses (£200,000). The following table shows the resource requirements and the estimated profit for each project. Use EXCEL’s Solver to answer question 1. 1. Suppose that CEO of company Z decides that project 2 and project 5 are mutually exclusive when all other projects remain independent. What is the revised project portfolio and the revised maximum profit?
Transeast Airlines flies planes on the following route:L.A.–Houston–N.Y.–Miami–L.A. The length (in miles) ofeach segment of this trip is as follows: L.A.–Houston, 1,500miles; Houston–N.Y., 1,700 miles; N.Y.–Miami, 1,300miles; Miami–L.A., 2,700 miles. At each stop, the planemay purchase up to 10,000 gallons of fuel. The price of fuelat each city is as follows: L.A., 88¢; Houston, 15¢; N.Y.,$1.05; Miami, 95¢. The plane’s fuel tank can hold at most12,000 gallons. To allow for the possibility of circling overa landing site, we require that the ending fuel level for eachleg of the flight be at least 600 gallons. The number ofgallons used per mile on each leg of the flight is1 (average fuel level on leg of flight/2,000)Review Problems 123To simplify matters, assume that the average fuel level onany leg of the flight isFormulate an LP that can be used to minimize the fuel costincurred in completing the schedule
Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:Department Product 1 Product 2 Product 3A 1.5 3 2B 2 1 2.5C 0.25 0.25 0.25During the next production period the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3. a. Formulate a linear programming model for maximizing total profit contribution. b. Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution?c. After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $400 for product 1, $550 for product 2, and $600 for product 3. If the solution developed in part…

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