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 40 gram of sulfur dioxide and 120 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5 grams of sulfur dioxide and 40 grams of particulate matter for each gallon produced. The compar 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 36,000 grams of sulfur dioxide and 90,000 grams of particulate matter daily, how many gallons of the chemical should be produced by each process to maximize daily profit? V is the maximum daily profit? Summarize the model. Maximize Objective function subject to V 36,000 Sulfur dioxide constraint V 90.000 Particulate constraint X, y 2 Nonnegative constraint Under the stated government regulations a maximum profit of S is obtained by producing V of product using the old process and V of product using the new process. (Type integers or decimals. Round to two decimal places as needed.)

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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 40 grams
of sulfur dioxide and 120 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5 grams of sulfur dioxide and 40 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 36,000 grams of sulfur dioxide and 90,000 grams of particulate matter daily, how many gallons of the chemical should be produced by each process to maximize daily profit? Wha
is the maximum daily profit? Summarize the model,
Maximize
Objective function
subject to
V 36,000
Sulfur dioxide constraint
V 90,000
Particulate constraint
х, у 2
Nonnegative constraint
Under the stated government regulations a maximum profit of $ is obtained by producing
of product using the old process and
of product using the new process.
(Type integers or decimals. Round to two decimal places as needed.)
(B) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 22,400 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
(Type integers or decimals. Round to two decimal places as needed.)
V of product using the old process and
V of product using the new process.
(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 other data remain unchanged.
Under these regulations a maximum profit of S is obtained by producing
(Type integers or decimals. Round to two decimal places as needed.)
of product using the old process and
of product using the new process.
Enter your answer in each of the answer boxes.
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 40 grams of sulfur dioxide and 120 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5 grams of sulfur dioxide and 40 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 36,000 grams of sulfur dioxide and 90,000 grams of particulate matter daily, how many gallons of the chemical should be produced by each process to maximize daily profit? Wha is the maximum daily profit? Summarize the model, Maximize Objective function subject to V 36,000 Sulfur dioxide constraint V 90,000 Particulate constraint х, у 2 Nonnegative constraint Under the stated government regulations a maximum profit of $ is obtained by producing of product using the old process and of product using the new process. (Type integers or decimals. Round to two decimal places as needed.) (B) Discuss the effect on the production schedule and the maximum profit if the government decides to restrict emissions of sulfur dioxide to 22,400 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 (Type integers or decimals. Round to two decimal places as needed.) V of product using the old process and V of product using the new process. (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 other data remain unchanged. Under these regulations a maximum profit of S is obtained by producing (Type integers or decimals. Round to two decimal places as needed.) of product using the old process and of product using the new process. Enter your answer in each of the answer boxes.
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