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Because of new federal regulations on pollution, a chemical plant introduced a new, more expensive process to supplement or replace an older process used in the production of a particular chemical. The older process emitted 30 grams of sulfur dioxide and 90 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5 grams of sulfur dioxide and 30 grams of particulate matter for each gallon produced. The company makes a profit of 80¢ per gallon and 20¢ per gallon on the old and new processes, respectively. Answer parts (A) through (C) below. (A) If the government allows the plant to emit no more than 25,500 grams of sulfur dioxide and 67,500 grams of particulate matter daily, how many gallons of the chemical should be produced by each process to maximize daily profit? What is the maximum daily profit? Summarize the model. Maximize subject to x, y2 25,500 67,500 0 Objective function Sulfur dioxide constraint Particulate constraint Nonnegative constraint Under the stated government regulations a maximum profit of $ is obtained by producing of product using the new process. (Type integers or decimals. Round to two decimal places as needed.) of product using the old process and (B) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 17,550 grams daily and al other data remain unchanged. Use a similar process to obtain the constraints for the new model. The maximum obtainable daily profit is now $ obtained by producing product using the new process. (Type integers or decimals. Round to two decimal places as needed.) (C) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 10,200 grams daily and al of product using the old process and of

Because of new federal regulations on pollution, a chemical plant introduced a new, more expensive process to supplement or replace an older process used in the production of a particular chemical. The older process emitted 30 grams of sulfur dioxide and 90 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5 grams of sulfur dioxide and 30 grams of particulate matter for each gallon produced. The company makes a profit of 80¢ per gallon and 20¢ per gallon on the old and new processes, respectively. Answer parts (A) through (C) below. (A) If the government allows the plant to emit no more than 25,500 grams of sulfur dioxide and 67,500 grams of particulate matter daily, how many gallons of the chemical should be produced by each process to maximize daily profit? What is the maximum daily profit? Summarize the model. Maximize subject to x, y2 25,500 67,500 0 Objective function Sulfur dioxide constraint Particulate constraint Nonnegative constraint Under the stated government regulations a maximum profit of $ is obtained by producing of product using the new process. (Type integers or decimals. Round to two decimal places as needed.) of product using the old process and (B) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 17,550 grams daily and al other data remain unchanged. Use a similar process to obtain the constraints for the new model. The maximum obtainable daily profit is now $ obtained by producing product using the new process. (Type integers or decimals. Round to two decimal places as needed.) (C) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 10,200 grams daily and al of product using the old process and of

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Because of new federal regulations on pollution, a chemical plant introduced a new, more expensive process to supplement or replace an older process used in the production of a particular chemical. The older process emitted 30 grams of sulfur dioxide and 90 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5 grams of sulfur dioxide and 30 grams of particulate matter for each gallon produced. The company makes a profit of 80¢ per gallon and 20¢ per gallon on the old and new processes, respectively. Answer parts (A) through (C) below. (A) If the government allows the plant to emit no more than 25,500 grams of sulfur dioxide and 67,500 grams of particulate matter daily, how many gallons of the chemical should be produced by each process to maximize daily profit? What is the maximum daily profit? Summarize the model. Maximize subject to x, y ≥ 25,500 67,500 0 Objective function Sulfur dioxide constraint Particulate constraint Nonnegative constraint is obtained by producing Under the stated government regulations a maximum profit of $ of product using the new process. (Type integers or decimals. Round to two decimal places as needed.) of product using the old process and (B) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 17,550 grams daily and all other data remain unchanged. Use a similar process to obtain the constraints for the new model. The maximum obtainable daily profit is now $ obtained by producing product using the new process. (Type integers or decimals. Round to two decimal places as needed.) (C) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 10,200 grams daily and all of product using the old process and of
Transcribed Image Text:Because of new federal regulations on pollution, a chemical plant introduced a new, more expensive process to supplement or replace an older process used in the production of a particular chemical. The older process emitted 30 grams of sulfur dioxide and 90 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5 grams of sulfur dioxide and 30 grams of particulate matter for each gallon produced. The company makes a profit of 80¢ per gallon and 20¢ per gallon on the old and new processes, respectively. Answer parts (A) through (C) below. (A) If the government allows the plant to emit no more than 25,500 grams of sulfur dioxide and 67,500 grams of particulate matter daily, how many gallons of the chemical should be produced by each process to maximize daily profit? What is the maximum daily profit? Summarize the model. Maximize subject to x, y ≥ 25,500 67,500 0 Objective function Sulfur dioxide constraint Particulate constraint Nonnegative constraint is obtained by producing Under the stated government regulations a maximum profit of $ of product using the new process. (Type integers or decimals. Round to two decimal places as needed.) of product using the old process and (B) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 17,550 grams daily and all other data remain unchanged. Use a similar process to obtain the constraints for the new model. The maximum obtainable daily profit is now $ obtained by producing product using the new process. (Type integers or decimals. Round to two decimal places as needed.) (C) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 10,200 grams daily and all of product using the old process and of
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