Please use the data below to answer Problem 10 on pages 351 to 352 in the textbook

Problems 351 the capital requirements, and the available capital funds over the next three years are sum; marized as follows: Capital Requirements ($1 Net Present Alternative Value ($) Year 1 Year 2 Year 3 Limited warehouse expansion 4,000 3,000 1,000 4,000 Extensive warehouse expansion 6,000 2,500 3,500 3,500 Test market new product 10,500 6,000 4,000 5,000 Advertising campaign 4,000 2,000 1,500 1,800 Basic research 8,000 5,000 1,000 4,000 Purchase new equipment 3,000 1,000 500 900 Capital funds available 10,500 7,000 8,750 a. Develop and solve an integer programming model for maximizing the net present value. b. Assume that only one of the warehouse expansion projects can be implemented. Mod- ify your model of part (a). 1'. Suppose that, if test marketing of the new product is carried out, the advertising cam- paign also must be conducted. Modify your formulation of part (b) to reect this new situation. 9. Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder auto- mobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2000, and the cost required to set up the production line for the 6-cylinder connecting rods is $3500. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to recongure the production line. Once the line has been set up, the weekly production capacities are 6000 6-cylinder connecting rods and 8000 4-cylinder connecting rods. Let x4 = the number of 4cylinder connecting rods produced next week x5 = the number of 6cylinder connecting rods produced next week 54 = 1 if the production line is set up to produce the 4cylinder connecting rods; 0 if otherwise Se : 1 if the production line is set up to produce the 6cylinder connecting rods; 0 if otherwise a. Using the decision variables x4 and :4, write a constraint that limits next week's pro- duction of the 4-cylinder connecting rods to either 0 or 8000 units. b. Using the decision variables x6 and 36, write a constraint that limits next week's pro- duction of the 6-cylinder connecting rods to either 0 or 6000 units. 1'. Write three constraints that, taken together, limit me production of connecting rods for next week. [1. Write an objective function for minimizing the cost of production for next week. 10. Grave City is considering the relocation of several police substations to obtain bet- ter enforcement in high-crime areas. The locations under consideration together Capyllgll 7.qu (engage Learmug All Rig)"; Reserved May not be copied. seminal orduplicalai. in whole or in pan Due in elem-mur- riglus. some [him perry coulenl may be suppressed from m: eanrur Mmefhsplcns]. Edilorial review has declined am my suppressed couleul does not malenully s'eer ure avcnll lclmilrg experience. Ceugage Learning reserves line right In mam-e additional content :1 my tune it' subsequent rights remit-rims 113qu it 352 Chapter 7 Integer Linear Programming with the areas that can be covered from these locations are given in the following table: Potential Locations for Substations Areas Covered 1, 5, 7 1, 2, 5, 7 1, 3, 5 2, 4, 5 3, 4, 6 4, 5,6 1, 5, 6, 7 . Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas. b. Solve the problem in part (a). 11. Hart Manufacturing makes three products. Each product requires manufacturing opera- tions in three departments: A, B, and C. The labor-hour requirements, by department, are as follows: Department Product 1 Product 2 Product 3 A 1.50 3.00 2.00 2.00 1.00 2.50 0.25 0.25 0.25 During 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 $600 for product 3. If the solu- tion developed in part (b) is to be used, what is the total profit contribution after taking into account the setup costs? d. Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 175 units of product 1, 150 units of product 2, or 140 units of product 3. e. Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced, and what is the projected total profit contribution? Com- pare this profit contribution to that obtained in part (c). 12. Offhaus Manufacturing produces office supplies but outsources the delivery of its prod- ucts to third-party carriers. Offhaus ships to 20 cities from its Dayton, Ohio, manufacture ing facility and has asked a variety of carriers to bid on its business. Seven carriers have responded with bids. The resulting bids (in dollars per truckload) are shown in the table. Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or Chapter($). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require itHide Folder Information Instructions Please use the data below to answer Problem 10 on pages 351 to 352 in the textbook. You need upload your Excel file into this Dropbox. Potential Locations for Substations Areas Covered D 1 , 5 , 7 B 2. 3, 9 m 0 0 4 , 6, 9 1, 2, 3 2, 4 . 6 6. 7. 8 5. 6. 9 3. 4. 5 1, 7 . 8