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QUESTION 1 25 pointsElectronics Play Group EPG of Packenham Ontario is considering how to distribute a new portable MP3 player they manufacture of which a first production run of 5000 units is now in progress in time for the Christmas season EPG expects to sell all 5000 units A strategy for distributing the new MP3 player involves deciding how many units to distribute among different markets These markets include 1 retail technology distributors eg Future Shop Best Buy The Source 2 retail business equipment distributors eg Business DepotStaples 3 retail commercial big box outlets eg WalMart and 4 direct online Internet purchases eg eBayProfits from the product will vary according to the distribution market because of differing costs of distribution As well advertising costs and personnel sales requirements by market also differ as per the table below The advertising budget is limited to 50000 and a maximum sales force time of 4600 hours is available Distribution ChannelProfit per UnitAdvertising Cost per UnitSales Effort per Unit751425 hours1 Technology T2 Business B639375 hours3 Commercial C5010380 hours4 Internet I447050 hourA contract with WalMart requires that at least 40 dozen 480 units new MP3 players be distributed there 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 EPGs market distribution problem is given belowLet T B C and I denote the number of units of the new MP3 player to distribute to Technology Business Commercial and Internet markets respectivelyMAX 75T63B50C44I Profits Subject to1 Advertising Budget 14T 9B 10C 7I 50000 2 Sales Effort Limit25T375B38C05I 4600 hrs 3 Production Limit TB C I5000 units4 Commercial Contract C 480 units5 NonnegativityT B C Iall0Consider the following problems a and b below Modify the formulation above to include the changes implied by the problems The problems a and b are to be considered independently Note you need only write the changes to the original formulationnot the entire formulationin the spaces belowaConsider the opportunity to purchase more hours for the sales effort There are up to 900 additional hours available at a cost of 1450 per hour Write down the revised formulation to account for this change 5 pointsSolution1 add a new decision variable SHE to denote additional sales effort hours 2 change constraint 2 25T375B38C05I 4600 hrs SHE 3 modify the Objective function add 1450SHE4 add upper bound constraint on new variable SHE900 hoursbEPG 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 TBC Write down the revised formulation to account for this change 4 pointsSolution1 Add a new constraint TTBC 075 or equivalent form
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