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2.2a Q6 1. Alumco manufactures aluminum sheets and aluminum bars. The maximum production capacity is estimated at either 800 sheets or 600 bars per day. The maximum daily demand is 550 sheets and 580 bars. The profit per ton is $40 per sheet and $35 per bar. Determine the optimal daily production mix. (Graphical method) 2,4B – Q8 2. Two products are manufactured sequentially on two machines. The time available on each machine is 8 hours per day and may be increased by up to 4 hours of overtime, if necessary, at an additional cost of $100 per hour. The following table gives the production rate on the two machines as well as the price per unit of the two products. Develop an LP model to determine the optimum production schedule and the recommended use of overtime, if any. Solve the problem using AMPL, Solver, or TORA. (Simplex) 2.4E – Q7 3. Hawaii Sugar Company produces brown sugar, processed (white) sugar, powdered sugar, and molasses from sugar cane syrup. The company purchases 4000 tons of syrup weekly and is contracted to deliver at least 25 tons weekly of each type of sugar. The production process starts by manufacturing brown sugar and molasses from the syrup. A ton of syrup produces .3 ton of brown sugar and .1 ton of molasses. White sugar is produced by processing brown sugar. It takes 1 ton of brown sugar to produce .8 ton of white sugar. Powdered sugar is produced from white sugar through a special grinding process that has a 95% conversion efficiency (1 ton of white sugar produces .95 ton of powdered sugar). The profits per ton for brown sugar, white sugar, powdered sugar, and molasses are $150, $200, $230, and $35, respectively. Formulate the problem as a linear program, and determine the weekly production schedule using AMPL, Solver, or TORA. 3.1B – Q3 4. JoShop manufactures three products whose unit profits are $2, $5, and $3, respectively. The company has budgeted 80 hours of labor time and 65 hours of machine time for the production of three products. The labor requirements per unit of products 1, 2, and 3 are 2, 1, and 2 hours, respectively. The corresponding machine-time requirements per unit are 1, 1, and 2 hours. JoShop regards the budgeted labor and machine hours as goals that may be exceeded, if necessary, but at the additional cost of $15 per labor hour and $10 per machine hour. Formulate the problem as LP, and determine its optimum solution using TORA, Solver, or AMPL. 3.3B – Q2 5. Consider the following set of constraints: Solve the problem for each of the following objective functions.
