Please help question 3!!!!

Case Study Second priority: commercial and industrial users that use natural gas as a source of raw material commercial and industrial users whereby natural gas is used as boiler fuel Third priority: Coastal States Chemicals and Fertilizers In December 2005, Bill Stock, general manager for the Louisiana Division of Coastal States Chemicals and Fertilizers, received a letter from Fred McNair of the Cajan Pipeline Company, which notified Coastal States that priorities had been estab- lished for the allocation of natural gas. The letter stated that Cajan Pipeline, the primary supplier of natural gas to Coastal States, might be instructed to curtail natural gas supplies to its industrial and commercial customers by as much as 40% dur- ing the ensuing winter months. Moreover, Cajan Pipeline had the approval of the Federal Power Commission (FPC) to curtail such supplies. Possible curtailment was attributed to the priorities estab- lished for the use of natural gas: Almost all of Coastal States' uses of natural gas were in the second and third priorities. Hence, its plants were certainly subject to brownouts, or natural gas curtailments. The occur- rence and severity of the brownouts depended on a number of complex factors. First, Cajan Pipeline was part of an interstate transmission network that delivered natural gas to residential and commercial buildings on the Atlantic coast and in North- eastern regions of the United States. Hence, the severity of the forthcoming winter in these regions would have a direct impact on the use of natural gas. First priority: residential and commercial heating CASE STUDY 251 or coal, Second, the demand for natural gas was soaring because it was the cleanest and most efficient fuel. There were almost no environmental problems in burning natural gas. Moreover, maintenance problems due to fuel-fouling in fireboxes and boilers were negligible with natural gas systems. Also, burn- ers were much easier to operate with natural gas than with oil Finally, the supply of natural gas was dwindling. The traditionally depressed price of natural gas had discouraged new exploration for gas wells; hence, shortages appeared imminent. Stock and his staff at Coastal States had been aware of the possibility of shortages of natural gas and had been investigat- ing ways of converting to fuel oil or coal as a substitute for natural gas. Their plans, however, were still in the develop mental stages. Coastal States required an immediate contin- gency plan to minimize the effect of a natural gas curtailment on its multiplant, operations. The obvious question was, what operations should be curtailed, and to what extent could the adverse effect upon profits be minimized? Coastal States had approval from the FPC and Cajan Pipeline to specify which of its plants would bear the burden of the curtailment if such cutbacks were necessary. McNair, of Cajan Pipeline, replied, "It's your pic': we don't care how you divide it if we make it was to minimize the impact on profits. After detailed discus- sion, the meeting was adjourned. Two weeks later, the meet- ing reconvened. At this session, the data in Table 8.3 were presented. Coastal States' contract with Cajan Pipeline specified a maximum natural gas consumption of 36,000,000 cubic feet per day for all six member plants. With these data, the tech- nical staff proceeded to develop a model that would specify changes in production rates in response to a natural gas curtail ment. (Curtailments are based on contracted consumption and not current consumption.) Discussion Questions 1. Develop a contingency model and specify the production rates for each product for (a) a 20% natural gas curtailment. (b) a 40% natural gas curtailment. 2. What impact will the natural gas shortage have on com- pany profits? 3. Develop the Sensitivity Report for the 20% natural gas curtailment model. Use this report to answer the following questions. Tiach question is independent of the others. (a) Interpret the shadow prices for the natural gas avail- ability constraint and for the two constraints that limit the maximum phosphoric acid and chlorine that Coastal can produce. (b) Brenda Lamb, Bill Stock's marketing manager, believes that due to increased competition she may have to decrease the unit profit contributions for all products by 3.5% each. What is the impact of this de- crease on the production values? On the total profit? (c) Jose Fernandez, Bill Stock's production manager, ke. thinks that he can increase the maximum production rate for chlorine and vinyl chloride monomer to 80% of capacity. For all other products, he thinks he can increase the maximum production rate to 100% of capacity. What would be the impact of this change on the total profit? smaller." The Model Six plants of Coastal States Louisiana Division were to sliare in the "pie." They were all located in the massive Baton Rouge Geismar-Gramercy industrial complex along the Mississippi River between Baton Rouge and New Orleans. Products man- ufactured at those plants that required significant amounts of natural gas were phosphoric acid, urea, ammonium phosphate, ammonium nitrate, chlorine, caustic soda, vinyl chloride monomer, and hydrofluoric acid. Stock called a meeting of members of his technical staff to discuss a contingency plan for allocation of natural gas among the products if a curtailment developed. The objective TABLE 8.3 Contribution to Profit and Overhead MAXIMUM PRODUCTION RATE (PERCENTAGE OF CAPACITY) CONTRIBUTION ($ PER TON) CAPACITY (TONS PER DAY) NATURAL GAS CONSUMPTION (1,000 CL.FT. PER TON) PRODUCT 400 60 80 5.5 80 250 80 300 90 90 100 300 100 Phosphoric acid Urea Ammonium phosphate Ammonium nitrate Chlorine Caustic soda Vinyl chloride monomer Hydrofluoric acid 50 . 800 1,000 500 60 60 7.0 8.0 10.0 15.0 16.0 12.0 11.0 50 65 60 70 400 80 52 CHAPTER 8 LINEAR PROGRAMMING SENSITIVITY ANALYSI (d) Bill Stock thinks he can persuade Coastal's Mississippi Division to give him 1,000,000 cubic feet of its allot- ment of natural gas from Cajan Pipeline. However, due to the Mississippi Division's pricing contract with Cajan Pipeline, this additional amount of natu- ral gas will cost Stock an additional $1.50 per 1,000 cubic feet (over current costs). Should Stock pursue this option? If so, what is the impact of this additional gas on his total profit? What is the impact if Bill Stock Case Study Second priority: commercial and industrial users that use natural gas as a source of raw material commercial and industrial users whereby natural gas is used as boiler fuel Third priority: Coastal States Chemicals and Fertilizers In December 2005, Bill Stock, general manager for the Louisiana Division of Coastal States Chemicals and Fertilizers, received a letter from Fred McNair of the Cajan Pipeline Company, which notified Coastal States that priorities had been estab- lished for the allocation of natural gas. The letter stated that Cajan Pipeline, the primary supplier of natural gas to Coastal States, might be instructed to curtail natural gas supplies to its industrial and commercial customers by as much as 40% dur- ing the ensuing winter months. Moreover, Cajan Pipeline had the approval of the Federal Power Commission (FPC) to curtail such supplies. Possible curtailment was attributed to the priorities estab- lished for the use of natural gas: Almost all of Coastal States' uses of natural gas were in the second and third priorities. Hence, its plants were certainly subject to brownouts, or natural gas curtailments. The occur- rence and severity of the brownouts depended on a number of complex factors. First, Cajan Pipeline was part of an interstate transmission network that delivered natural gas to residential and commercial buildings on the Atlantic coast and in North- eastern regions of the United States. Hence, the severity of the forthcoming winter in these regions would have a direct impact on the use of natural gas. First priority: residential and commercial heating CASE STUDY 251 or coal, Second, the demand for natural gas was soaring because it was the cleanest and most efficient fuel. There were almost no environmental problems in burning natural gas. Moreover, maintenance problems due to fuel-fouling in fireboxes and boilers were negligible with natural gas systems. Also, burn- ers were much easier to operate with natural gas than with oil Finally, the supply of natural gas was dwindling. The traditionally depressed price of natural gas had discouraged new exploration for gas wells; hence, shortages appeared imminent. Stock and his staff at Coastal States had been aware of the possibility of shortages of natural gas and had been investigat- ing ways of converting to fuel oil or coal as a substitute for natural gas. Their plans, however, were still in the develop mental stages. Coastal States required an immediate contin- gency plan to minimize the effect of a natural gas curtailment on its multiplant, operations. The obvious question was, what operations should be curtailed, and to what extent could the adverse effect upon profits be minimized? Coastal States had approval from the FPC and Cajan Pipeline to specify which of its plants would bear the burden of the curtailment if such cutbacks were necessary. McNair, of Cajan Pipeline, replied, "It's your pic': we don't care how you divide it if we make it was to minimize the impact on profits. After detailed discus- sion, the meeting was adjourned. Two weeks later, the meet- ing reconvened. At this session, the data in Table 8.3 were presented. Coastal States' contract with Cajan Pipeline specified a maximum natural gas consumption of 36,000,000 cubic feet per day for all six member plants. With these data, the tech- nical staff proceeded to develop a model that would specify changes in production rates in response to a natural gas curtail ment. (Curtailments are based on contracted consumption and not current consumption.) Discussion Questions 1. Develop a contingency model and specify the production rates for each product for (a) a 20% natural gas curtailment. (b) a 40% natural gas curtailment. 2. What impact will the natural gas shortage have on com- pany profits? 3. Develop the Sensitivity Report for the 20% natural gas curtailment model. Use this report to answer the following questions. Tiach question is independent of the others. (a) Interpret the shadow prices for the natural gas avail- ability constraint and for the two constraints that limit the maximum phosphoric acid and chlorine that Coastal can produce. (b) Brenda Lamb, Bill Stock's marketing manager, believes that due to increased competition she may have to decrease the unit profit contributions for all products by 3.5% each. What is the impact of this de- crease on the production values? On the total profit? (c) Jose Fernandez, Bill Stock's production manager, ke. thinks that he can increase the maximum production rate for chlorine and vinyl chloride monomer to 80% of capacity. For all other products, he thinks he can increase the maximum production rate to 100% of capacity. What would be the impact of this change on the total profit? smaller." The Model Six plants of Coastal States Louisiana Division were to sliare in the "pie." They were all located in the massive Baton Rouge Geismar-Gramercy industrial complex along the Mississippi River between Baton Rouge and New Orleans. Products man- ufactured at those plants that required significant amounts of natural gas were phosphoric acid, urea, ammonium phosphate, ammonium nitrate, chlorine, caustic soda, vinyl chloride monomer, and hydrofluoric acid. Stock called a meeting of members of his technical staff to discuss a contingency plan for allocation of natural gas among the products if a curtailment developed. The objective TABLE 8.3 Contribution to Profit and Overhead MAXIMUM PRODUCTION RATE (PERCENTAGE OF CAPACITY) CONTRIBUTION ($ PER TON) CAPACITY (TONS PER DAY) NATURAL GAS CONSUMPTION (1,000 CL.FT. PER TON) PRODUCT 400 60 80 5.5 80 250 80 300 90 90 100 300 100 Phosphoric acid Urea Ammonium phosphate Ammonium nitrate Chlorine Caustic soda Vinyl chloride monomer Hydrofluoric acid 50 . 800 1,000 500 60 60 7.0 8.0 10.0 15.0 16.0 12.0 11.0 50 65 60 70 400 80 52 CHAPTER 8 LINEAR PROGRAMMING SENSITIVITY ANALYSI (d) Bill Stock thinks he can persuade Coastal's Mississippi Division to give him 1,000,000 cubic feet of its allot- ment of natural gas from Cajan Pipeline. However, due to the Mississippi Division's pricing contract with Cajan Pipeline, this additional amount of natu- ral gas will cost Stock an additional $1.50 per 1,000 cubic feet (over current costs). Should Stock pursue this option? If so, what is the impact of this additional gas on his total profit? What is the impact if Bill Stock