SMP&P is a fully integrated paper company with extensive holdings in woodlands, several large mills, and nationwide distribution facilities. The company manufactures a wide variety of paper products under its own brand name, and a more limited product line under contract for private distributors. SMP&P's oldest mill, Bayou 1, is located in Pass Christian, Mississippi and produces four major products, book paper, coarse paper, container board and food board. The flow of materials through the mill is illustrated below: BEATING CHIPPING KRAFT PULPING MACHINING hardwood BLEACHING book paper coarse paper softwood container board SEMI-CHEMICAL PULPING food board PROCESS DESCRIPTION The milling process begins with chipping in which two different grades of hardwood and one type grade of softwood are used as inputs. After chipping, the hardwood outputs enter Kraft pulping or semi-chemical pulping. The softwood and hardwood outputs from chipping enter the Kraft pulping operation. Some of the hardwood outputs from chipping transverse through semi chemical pulping process. No softwood chipping outputs can enter semi chemical pulping. From Kraft pulping, some products enter the bleaching stage while others go directly through beating. Semi-chemical pulping products go directly to the beating stage process. The outputs of the beating process are inputs into machining which produces the four major products, book paper, coarse paper, container board and food board. Hardwood and softwood inputs for chipping are available from internal company sources in limited quantities. Additional quantities can be purchased at a slightly higher cost. The related availability's and costs are as follows: INTERNAL SOURCES IN TONS PER YEAR INTERNAL COST EXTERNAL COST WOOD TYPE Hardwood - grade 1 125.000 tons per year Hardwood - grade 2 200,000 tons per year Softwood 160,000 tons per year $19 per ton $21.10 per ton $20 per ton $25.64 per ton $22.50 per ton $ 20.95 per ton When required, up to 30.000 tons per year of Softwood Kraft Pulp can be purchased at a cost of $59/ton. This purchased pulp cannot be bleached and is used as an input into the beating process. The following process yields (tons output/tons input) and capacities (tons input/year) were provided by the operations manager: YIELDS HARDWOOD-2 PROCESS HARDWOOD - 1 SOFTWOOD CAPACITIES .87 .88 Chipping .954 Kraft Pulping .92 Semi- Chemical Pulping 765 Bleaching .821 Beating .99 Machining 93 .95 .645 .831 600,000 400,000 300,000 490,000 400,000 485,000 .99 .825 99 .98 .98 98 MARKET DEMANDS & OTHER REQUIREMENTS The four final products must be composed of at least 25% of grade 1 hardwood and at least 50% softwood. At least 20% of the composition must consist of outputs from the bleaching process and at least 10% from the kraft pulping process (not including the kraft pulping that is bleached. The four products must consist of no more than 60% of semi-chemical hardwood outputs. Due to contractual requirements a minimum of 33.400 tons of coarse paper, 117,800 tons of container board and 61,500 tons of food board must be produced in the upcoming year. SMP&P marketing has determined that all of the book paper that can be produced will be sold as well as any excess of the other three products above their minimum requirement. Company records show that variable operating cost (S/ton input) for each process are defined as follows: PROCESS OPERATING COST Chipping Kraft Pulping Semi- Chemical Pulping Bleaching Beating Machining $ 3.40 per ton S 13.12 per ton $ 18.98 per ton S 9.08 per ton $ 77 per ton $ 7.16 per ton Book paper sells for $210 per ton, S 125 per ton for coarse paper, $133 per ton for container board and $128 per ton for food board. QUESTIONS a. Develop and solve a linear programming model to determine output and input requirements which will maximize profits. b. Senior management is considering implementing modifications to the Bayou 1 plant to increase output capacity. Due to budget constraints only one operation or process can be modified. The cost of increasing capacity is approximately the same for each operation and would result an increase of capacity up to 10%. Which operation (process) would you recommend to increase capacity? Support your answer with analysis. Stay within the confines and sensitivities of the existing problem. In other words, do not provide a second run in lindo to support your analysis. Rather, rationalize from observation of the sensitivity analysis within the existing lindo output. C. A supplier is interested in selling SMP&P 10,000 tons of Softwood Kraft pulp at a cost of $625.000. Should SMP&P accept this offer? Why? SMP&P is a fully integrated paper company with extensive holdings in woodlands, several large mills, and nationwide distribution facilities. The company manufactures a wide variety of paper products under its own brand name, and a more limited product line under contract for private distributors. SMP&P's oldest mill, Bayou 1, is located in Pass Christian, Mississippi and produces four major products, book paper, coarse paper, container board and food board. The flow of materials through the mill is illustrated below: BEATING CHIPPING KRAFT PULPING MACHINING hardwood BLEACHING book paper coarse paper softwood container board SEMI-CHEMICAL PULPING food board PROCESS DESCRIPTION The milling process begins with chipping in which two different grades of hardwood and one type grade of softwood are used as inputs. After chipping, the hardwood outputs enter Kraft pulping or semi-chemical pulping. The softwood and hardwood outputs from chipping enter the Kraft pulping operation. Some of the hardwood outputs from chipping transverse through semi chemical pulping process. No softwood chipping outputs can enter semi chemical pulping. From Kraft pulping, some products enter the bleaching stage while others go directly through beating. Semi-chemical pulping products go directly to the beating stage process. The outputs of the beating process are inputs into machining which produces the four major products, book paper, coarse paper, container board and food board. Hardwood and softwood inputs for chipping are available from internal company sources in limited quantities. Additional quantities can be purchased at a slightly higher cost. The related availability's and costs are as follows: INTERNAL SOURCES IN TONS PER YEAR INTERNAL COST EXTERNAL COST WOOD TYPE Hardwood - grade 1 125.000 tons per year Hardwood - grade 2 200,000 tons per year Softwood 160,000 tons per year $19 per ton $21.10 per ton $20 per ton $25.64 per ton $22.50 per ton $ 20.95 per ton When required, up to 30.000 tons per year of Softwood Kraft Pulp can be purchased at a cost of $59/ton. This purchased pulp cannot be bleached and is used as an input into the beating process. The following process yields (tons output/tons input) and capacities (tons input/year) were provided by the operations manager: YIELDS HARDWOOD-2 PROCESS HARDWOOD - 1 SOFTWOOD CAPACITIES .87 .88 Chipping .954 Kraft Pulping .92 Semi- Chemical Pulping 765 Bleaching .821 Beating .99 Machining 93 .95 .645 .831 600,000 400,000 300,000 490,000 400,000 485,000 .99 .825 99 .98 .98 98 MARKET DEMANDS & OTHER REQUIREMENTS The four final products must be composed of at least 25% of grade 1 hardwood and at least 50% softwood. At least 20% of the composition must consist of outputs from the bleaching process and at least 10% from the kraft pulping process (not including the kraft pulping that is bleached. The four products must consist of no more than 60% of semi-chemical hardwood outputs. Due to contractual requirements a minimum of 33.400 tons of coarse paper, 117,800 tons of container board and 61,500 tons of food board must be produced in the upcoming year. SMP&P marketing has determined that all of the book paper that can be produced will be sold as well as any excess of the other three products above their minimum requirement. Company records show that variable operating cost (S/ton input) for each process are defined as follows: PROCESS OPERATING COST Chipping Kraft Pulping Semi- Chemical Pulping Bleaching Beating Machining $ 3.40 per ton S 13.12 per ton $ 18.98 per ton S 9.08 per ton $ 77 per ton $ 7.16 per ton Book paper sells for $210 per ton, S 125 per ton for coarse paper, $133 per ton for container board and $128 per ton for food board. QUESTIONS a. Develop and solve a linear programming model to determine output and input requirements which will maximize profits. b. Senior management is considering implementing modifications to the Bayou 1 plant to increase output capacity. Due to budget constraints only one operation or process can be modified. The cost of increasing capacity is approximately the same for each operation and would result an increase of capacity up to 10%. Which operation (process) would you recommend to increase capacity? Support your answer with analysis. Stay within the confines and sensitivities of the existing problem. In other words, do not provide a second run in lindo to support your analysis. Rather, rationalize from observation of the sensitivity analysis within the existing lindo output. C. A supplier is interested in selling SMP&P 10,000 tons of Softwood Kraft pulp at a cost of $625.000. Should SMP&P accept this offer? Why