Answered: A, What is the linear programming model…

Business

Operations Management

A, What is the linear programming model for this problem? Decision Variables: LP Model:

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 43P

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he North Shore Bank is working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank, including adequate customer service, employee breaks, and so on. On Fridays, the bank is open from 9:00 a.m. to 7:00 p.m. The number of tellers necessary to provide adequate customer service during each hour of operation is summarized as follows: Each full-time employee starts on the hour and works a 4-hour shift, followed by a 1-hour break and then a 3-hour shift. Part-time employees work one 4-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $15 per hour ($105 a day), and part-time employees cost the bank $8 per hour ($32 per day). a. Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost. (Hint: Let xi= number of full-time employees coming on duty at the beginning of…
Please use excel for this problem A furniture manufacturer produces two types of tables – country and contemporary – using three types of machines. The time required to produce the tables on each machine is given in the following table: Machine Country Contemporary Total Machine Time Available Per Week Router 3.5 4.0 1,000 Sander 4.5 6.5 2,000 Polisher 3.0 2.0 1,500 Country tables sell for $395 and contemporary tables sell for $515. Management has determined that at least 25% of the tables made should be country and at least 38% should be contemporary. How many of each type of table should the company manufacture if it wants to maximize its revenue? Formulate an LP model for this problem Create the spreadsheet model and use Solver to solve the problem.
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Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 52 units of synthetic fiber, requires 28 hours of production time, and needs 22 units of foam backing. Each roll of Grade Y carpet uses 45 units of synthetic fiber, requires 30 hours of production time, and needs 16 units of foam backing.The profit per roll of Grade X carpet is $205 and the profit per roll of Grade Y carpet is $155. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility. This means that instead of using the = or ≤ sign in the constraint you should use the ≥ sign.). The company has 1500 units of foam backing available for use.Develop and solve a linear programming model…
Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber, requires 28 hours of production time, and needs 15 units of foam backing.The profit per roll of Grade X carpet is $200 and the profit per roll of Grade Y carpet is $160. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use.Develop a linear programming model for this problem.1. Define the Decision Variables2. Write the Objective3. Write the Constraints
Nkrumah Farms encompasses 900 acres, and is planning to grow groundnut, soybeans, corn, and wheat in the coming planting season. Fertilizer costs per acre are: Ghs 3 for groundnut, Ghc 5 for soybeans, Ghs 2 for corn, and Ghs 1 for wheat. Nkrumah Farms estimate that each acre of groundnut will require an average of 4 hours of labour per week, while soybeans will require an average of 5 hours of labor per week. Corn and wheat will each require an average of 2 hours per week. Based on past yields and current market prices, Nkrumah Farms estimate a profit of Ghs 1200 for each acre of groundnut, Ghs 3,000 for each acre of soybeans, Ghs 2,000 for each acre of corn, and Ghs 1,000 for each acre of wheat. Nkrumah Farms cannot afford to spend more than Ghs 3,000 on fertilizer. In addition, local labor regulations require Nkrumah Farms to utilize at least 2,200 hours of labour per week.Based on past demands, Nkrumah Farms would also want to ensure that the number of acres allocated to wheat…
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