Can you help me solve the below problem with linear programming method? Please provide me all the linear equation for curtailment plan on 20% and 40%.

Also what recommendations/options should be suggested to Barco?

The General Manager of the Texas Division of BarCo Corporation, received notification from MaxEnergy that natural gas supplies were being rapidly depleted. In the event of a shortage, MaxEnergy, the main producer and distributor of natural gas in the Gulf South region, would allocate gas to its customers under the following provisions established by the Federal Commission: 1. First Priority: Residential and commercial heating and cooling 2. Second Priority: Commercial and industrial firms that use natural gas as a source of raw material 3. Third Priority: Industrial firms that use natural gas as a boiler fuel In the communication, it was mentioned that most of BarCo's uses were in the second and third priority classifications. Hence, BarCo would probably be subjected to "rolling brownouts", temporary and periodic curtailments of natural gas supplies. MaxEnergy planned to monitor its pipeline pressures and order reductions to maintain minimum levels. MaxEnergy preferred that its customers initiate the reduction process to minimize the effect on their industrial processes. MaxEnergy was authorized, however, to curtail supplies unilaterally if pipeline pressure fell below minimum levels. The natural gas shortage was created by the unprecedented heat wave of the summer of 2019. Electrical generating plants were operating at capacity to supply electricity to operate air conditioning and refrigeration units. Although long-range plans called for these utility companies to convert to coal, oil, or nuclear fuel, natural gas remained the dominant boiler fuel. CURTAILMENT PLAN BarCo's problem was to determine which of its complexes would be least affected by a gas curtailment. Its Texas Division is located in the greater Houston area; plants are located in the suburbs of Deer Park and Battleground. Both of these areas would be included in the curtailment region in the event of a brownout. Except for BarCo's ammonia operations, all gas purchased was used as boiler fuel. In its ammonia plant, gas was used as a source of raw materials. (The manufacture of ammonia uses natural gas in the steam reforming process). In a detailed discussion with the CEO of MaxEnergy, BarCo learned that MaxEnergy would not specify the products to be curtailed. The curtailment procedure would be based primarily on a customer's usage pattern. Hence, BarCo had the flexibility to absorb curtailments where they would have minimum impact on profits. Based on this information, BarCo called a staff meeting to discuss a contingency plan for allocation of natural gas among the firm's products if curtailments became a reality. The specific objective was to minimize the impact on profits/overhead contribution. After a week of study, the information in Tables 1 and 2 was presented to BarCo management. Table 1: Contribution to profit $/Ton 80 120 140 Product Ammonia Ammonium phosphate Ammonium nitrate Urea Hydrofluoric acid Chlorine Caustic soda Vinyl chloride monomer 140 90 70 60 90 Table 2: Operational data Product Capacity (tons/day) Production Rate (% of capacity) Natural Gas Consumption (1,000 cu. ft./ton) 8.0 1,500 80 600 90 10.0 70 80 Ammonia Ammonium phosphate Ammonium nitrate Urea Hydrofluoric acid Chlorine Caustic soda Vinyl chloride monomer 700 200 800 1,500 1,600 70 80 80 12.0 12.0 7.0 18.0 20.0 1,400 60 14.0 BarCo's contract with MaxEnergy specified a maximum of 90,000 cu.ft. X 103 per day for its complexes. However, curtailments are projected to be based on actual usage rather than contractual xim The current natural gas usage is 85,680 cu. ft. x 103 per day. MaxEnergy projects curtailments in the range of 20 to 40 percent. Business Report 1. Define the business problem 2. Formulate a linear program for 20 and 40% curtailment of natural gas usage. 3. Discuss the sensitivity analysis 4. Provide a discussion of BarCo's options and your recommendations for action The General Manager of the Texas Division of BarCo Corporation, received notification from MaxEnergy that natural gas supplies were being rapidly depleted. In the event of a shortage, MaxEnergy, the main producer and distributor of natural gas in the Gulf South region, would allocate gas to its customers under the following provisions established by the Federal Commission: 1. First Priority: Residential and commercial heating and cooling 2. Second Priority: Commercial and industrial firms that use natural gas as a source of raw material 3. Third Priority: Industrial firms that use natural gas as a boiler fuel In the communication, it was mentioned that most of BarCo's uses were in the second and third priority classifications. Hence, BarCo would probably be subjected to "rolling brownouts", temporary and periodic curtailments of natural gas supplies. MaxEnergy planned to monitor its pipeline pressures and order reductions to maintain minimum levels. MaxEnergy preferred that its customers initiate the reduction process to minimize the effect on their industrial processes. MaxEnergy was authorized, however, to curtail supplies unilaterally if pipeline pressure fell below minimum levels. The natural gas shortage was created by the unprecedented heat wave of the summer of 2019. Electrical generating plants were operating at capacity to supply electricity to operate air conditioning and refrigeration units. Although long-range plans called for these utility companies to convert to coal, oil, or nuclear fuel, natural gas remained the dominant boiler fuel. CURTAILMENT PLAN BarCo's problem was to determine which of its complexes would be least affected by a gas curtailment. Its Texas Division is located in the greater Houston area; plants are located in the suburbs of Deer Park and Battleground. Both of these areas would be included in the curtailment region in the event of a brownout. Except for BarCo's ammonia operations, all gas purchased was used as boiler fuel. In its ammonia plant, gas was used as a source of raw materials. (The manufacture of ammonia uses natural gas in the steam reforming process). In a detailed discussion with the CEO of MaxEnergy, BarCo learned that MaxEnergy would not specify the products to be curtailed. The curtailment procedure would be based primarily on a customer's usage pattern. Hence, BarCo had the flexibility to absorb curtailments where they would have minimum impact on profits. Based on this information, BarCo called a staff meeting to discuss a contingency plan for allocation of natural gas among the firm's products if curtailments became a reality. The specific objective was to minimize the impact on profits/overhead contribution. After a week of study, the information in Tables 1 and 2 was presented to BarCo management. Table 1: Contribution to profit $/Ton 80 120 140 Product Ammonia Ammonium phosphate Ammonium nitrate Urea Hydrofluoric acid Chlorine Caustic soda Vinyl chloride monomer 140 90 70 60 90 Table 2: Operational data Product Capacity (tons/day) Production Rate (% of capacity) Natural Gas Consumption (1,000 cu. ft./ton) 8.0 1,500 80 600 90 10.0 70 80 Ammonia Ammonium phosphate Ammonium nitrate Urea Hydrofluoric acid Chlorine Caustic soda Vinyl chloride monomer 700 200 800 1,500 1,600 70 80 80 12.0 12.0 7.0 18.0 20.0 1,400 60 14.0 BarCo's contract with MaxEnergy specified a maximum of 90,000 cu.ft. X 103 per day for its complexes. However, curtailments are projected to be based on actual usage rather than contractual xim The current natural gas usage is 85,680 cu. ft. x 103 per day. MaxEnergy projects curtailments in the range of 20 to 40 percent. Business Report 1. Define the business problem 2. Formulate a linear program for 20 and 40% curtailment of natural gas usage. 3. Discuss the sensitivity analysis 4. Provide a discussion of BarCo's options and your recommendations for action