4.A company produces stereo speakers of two sizes and anticipates demand for the first three months of the year at the levels shown in the following table Large 200 January February March Small 400 500 550 320 400 A production manager has computed that each month, during normal working time, capacity dictates that 2(Number of Small Speakers) + Number of Large Speakers s 1200 However, some overtime can be worked, production during these additional hours each month being constrained by: [Number of Small Speakers) + Number of Large Speakers S 240 For normal working time, it costs $60 to produce each small speaker and $80 for each large speaker. However, for overtime working, these figures rise to $70 and $95, respectively. Further, it is computed that for each month a small speaker is held inn inventory an additional cost of $3 is incurred, while the corresponding figure for large speakers is $5. The objective of this corporation is to find the lowest-cost, feasible production schedule that will allow demand to be fully satisfied in each of the three months. We will define our decision variablesex1,x2,...,x24-cach refers to the quantity of one or the other speaker to be produced in a given month, either in normal time or overtime, and to be sold in a specific month. For example, x17 = the number of small speakers to be produced in normal time in February and sold in March, and x 12 = the number of large speakers to be produced in overtime in January and sold in March PRODUCTION SALE JANUARY Small Large FEBRUARY Small Large x5 x6 MARCH Small Large January: Normal Small Overtime Small Normal Large Overtime Large X8 February: Normal Small Overtime Small Normal Large Overtime Large x13 x14 x15 x16 March: Normal Small Overtime Small Normal Large Overtime Large Here are the unit costs (in dollars) associated with the decision variables PRODUCTION SALE JANUARY Small Large FEBRUARY Small Large MARCH Small Large 60 January: Normal Small Overtime Small Normal Large Overtime Large 63 66 76 90 105 February: Normal Small Overtime Small Normal Large Overtime Large March: Normal Small Overtime Small Normal Large Overtime Large Write out the LP for this problem 4.A company produces stereo speakers of two sizes and anticipates demand for the first three months of the year at the levels shown in the following table Large 200 January February March Small 400 500 550 320 400 A production manager has computed that each month, during normal working time, capacity dictates that 2(Number of Small Speakers) + Number of Large Speakers s 1200 However, some overtime can be worked, production during these additional hours each month being constrained by: [Number of Small Speakers) + Number of Large Speakers S 240 For normal working time, it costs $60 to produce each small speaker and $80 for each large speaker. However, for overtime working, these figures rise to $70 and $95, respectively. Further, it is computed that for each month a small speaker is held inn inventory an additional cost of $3 is incurred, while the corresponding figure for large speakers is $5. The objective of this corporation is to find the lowest-cost, feasible production schedule that will allow demand to be fully satisfied in each of the three months. We will define our decision variablesex1,x2,...,x24-cach refers to the quantity of one or the other speaker to be produced in a given month, either in normal time or overtime, and to be sold in a specific month. For example, x17 = the number of small speakers to be produced in normal time in February and sold in March, and x 12 = the number of large speakers to be produced in overtime in January and sold in March PRODUCTION SALE JANUARY Small Large FEBRUARY Small Large x5 x6 MARCH Small Large January: Normal Small Overtime Small Normal Large Overtime Large X8 February: Normal Small Overtime Small Normal Large Overtime Large x13 x14 x15 x16 March: Normal Small Overtime Small Normal Large Overtime Large Here are the unit costs (in dollars) associated with the decision variables PRODUCTION SALE JANUARY Small Large FEBRUARY Small Large MARCH Small Large 60 January: Normal Small Overtime Small Normal Large Overtime Large 63 66 76 90 105 February: Normal Small Overtime Small Normal Large Overtime Large March: Normal Small Overtime Small Normal Large Overtime Large Write out the LP for this
