Linear Programming.docx

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Wojtek Michalowski

Linear Programming Distribtution Channel Prof. Per Unit Cost Per unit Sales Effort per unit 1 Tech (T) 75 14 2.5 hours 2. Business (B) 63 9 3.75 hours 3. Commercial 50 10 3.8 hours 4. Internet (I) 44 7 0.5 hours Electronics Play Group (EPG) of Packenham, Ontario is considering how to distribute a new portable MP3 player they manufacture. EPG expects to sellall 5,000 units. These markets include: (1) retail technology distributors (e.g., Future Shop, Best Buy, The Source); (2) retail business equipment distributors (e.g., Business Depot/Staples); (3) retail commercial big box outlets(e.g., WalMart); and (4) direct on line Internet purchases (e.g., eBay).Profits from the product will vary according to the distribution market because of differing costs ofdistribution. As well, advertising costs and personnel sales requirements by market also differ as per the table below. The advertising budget is limited to $50,000 and a maximum sales force time of4,600 hours is available. A contract with WalMart requires that at least 40 dozen (480 units) new MP3 players be distributedthere. The company wants to establish a distribution strategy to maximize total expected profits from the distribution of the new MP3 player. The correct linear programing formulation for EPG’smarket distribution problem is given below: MAX75T + 63B + 50C +44I Subject to 1. Advertising Budget: 14T + 9B + 10C + 7I 0 (a)Consider the opportunity to purchase more hours for the sales effort. There are up to 900additional hours available at a cost of $14.50 per hour. Write down the revised formulation toaccount for this change. (b)EPG wants to ensure that their distribution of the MP3 product in the technology retail stores (T)is at least 75% of total distribution in all the retail stores (T+B+C). (c) From the optimal solution, what are the sales effort allocations to each of the distribution channels? (4 points) d) What would need to happen to the Business distribution option unit profits before it would be optimal to acquire an advertising and sales force allocation of its own? (4 points) (e) Given the highly competitive markets for MP3 players in 2005, EPG was considering committing more financial resources to support the advertising costs for this project. After some discussion, the Board of Directors approved another $12,000 for this project. What will be the impact on the new optimal profit of these new operating funds for advertising? (f) Given a high volume of sales in early December, Wal-Mart has sent a memo to EPG requesting that the current contract be renegotiated so that the 480 units be increased by 144 more units. Determine the impact on EPG’s total optimal profit if the new terms of the contract go into effect. (4 points) Binary/Integer Programming DWR Ltd has MADE new game consoles: zbox and ybox. Production lines cost $25,000 for zbox and $32,000 for ybox. Each console has profits: $150/unit for zbox and $210/unit for ybox. DWR Ltd has space for creating 3 production lines capable of manufacturing the consoles and each line can be used to manufacture both consoles at the same time. However, management has decided that in order to mitigate the risks, only one production line would be open. zbox can be produced at the rate of 15 units/hr on line 1, 18 units/hr on line 2, and 22 units/hr on line 3. Ybox can be produced at the rate of 20 units/hr, 17 units/hr, and 10 units/hr respectively. Line 1 has 340 hours production capacity, line 2 has 400 hrs, line 3= 380 hours capacity. Write in mixed binary integer programming problem. DO NOT SOLVE. Goal Programming Smafs frams Labor hrs needed
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