Pollution Control Because of new federal regulations on pollution, a chemical plant introduced a new and more expensive process to supplement or replace an older process used in the pr and 40 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5 grams of sulfur dioxide and 20 grams of particulate matter into the at per gallon on the old process and 20 cents per gallon on the new process. If the government allows the plant to emit no more than 16,000 grams of sulfur dioxide and 30,000 grams of partic produced by each process to maximize daily profit? What is the daily profit? Let o = the number of gallons of the chemical produced by the old process, and Let n = the number of gallons of the chemical produced by the new process Which option (a, b, c, or d) shows the correct objective function and constraints for this application? O Objective Function: Maximize Profit, P = 0.20% +0.60* Constraints: 200+5n> 16000, 400 + 20n <= 30000, >= 0, >=0 O Objective Function: Maximize Profit, P = 0.60*o +0.20* Constraints: 200 + 5n>=30000, 400 + 20n>= 16000, o>= 0, >= 0 O Objective Function: Maximize Profit, P = 0.60*o +0.20* Constraints: 200 +5n<= 16000, 400 + 20n <=30000, o>= 0, >= 0 O Objective Function: Maximize Profit, P=0.60*o +0.20 Constraints: 400+5n <= 30000, 200 + 20n <= 16000, o >= 0, n>= 0
Pollution Control Because of new federal regulations on pollution, a chemical plant introduced a new and more expensive process to supplement or replace an older process used in the pr and 40 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5 grams of sulfur dioxide and 20 grams of particulate matter into the at per gallon on the old process and 20 cents per gallon on the new process. If the government allows the plant to emit no more than 16,000 grams of sulfur dioxide and 30,000 grams of partic produced by each process to maximize daily profit? What is the daily profit? Let o = the number of gallons of the chemical produced by the old process, and Let n = the number of gallons of the chemical produced by the new process Which option (a, b, c, or d) shows the correct objective function and constraints for this application? O Objective Function: Maximize Profit, P = 0.20% +0.60* Constraints: 200+5n> 16000, 400 + 20n <= 30000, >= 0, >=0 O Objective Function: Maximize Profit, P = 0.60*o +0.20* Constraints: 200 + 5n>=30000, 400 + 20n>= 16000, o>= 0, >= 0 O Objective Function: Maximize Profit, P = 0.60*o +0.20* Constraints: 200 +5n<= 16000, 400 + 20n <=30000, o>= 0, >= 0 O Objective Function: Maximize Profit, P=0.60*o +0.20 Constraints: 400+5n <= 30000, 200 + 20n <= 16000, o >= 0, n>= 0
Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Transcribed Image Text:Pollution Control Because of new federal regulations on pollution, a chemical plant introduced a new and more expensive process to supplement or replace an older process used in the production of a particular chemical. The older process emitted 20 grams of sulfur dioxide
and 40 grams of particulate matter into the atmosphere for each gallon of chemical produced. The new process emits 5 grams of sulfur dioxide and 20 grams of particulate matter into the atmosphere for each gallon of chemical produced. The company makes a profit of 60 cents
per gallon on the old process and 20 cents per gallon on the new process. If the government allows the plant to emit no more than 16,000 grams of sulfur dioxide and 30,000 grams of particulate matter into the atmosphere daily, how many gallons of the chemical should be
produced by each process to maximize daily profit? What is the daily profit?
Let o = the number of gallons of the chemical produced by the old process, and
Let n = the number of gallons of the chemical produced by the new process
Which option (a, b, c, or d) shows the correct objective function and constraints for this application?
O Objective Function: Maximize Profit, P = 0.20*o + 0.60*n
Constraints: 200 + 5n >= 16000, 400 + 20n <= 30000, o >= 0, n>= 0
O Objective Function: Maximize Profit, P = 0.60*o + 0.20*n
Constraints: 200 + 5n >= 30000, 400 + 20n >= 16000, o >= 0, n>= 0
O Objective Function: Maximize Profit, P = 0.60*o + 0.20*n
Constraints: 200 + 5n <= 16000, 400 + 20n <= 30000, o >= 0, n>= 0
O Objective Function: Maximize Profit, P = 0.60*o + 0.20*n
Constraints: 400 + 5n <= 30000, 200 + 20n <= 16000, o >= 0, n>= 0
Expert Solution
Step 1
The formulation of a linear program starts with the formulation of a mathematical model that has variables and constraints, which are typically represented by linear inequalities. These inequalities define the feasible region of the problem, which is defined as all points that satisfy all constraints and at least one variable constraint. The objective function defines what type of value we are looking for in our models, such as profit or cost. The optimal solution for this type of function will be where the objective function reaches its maximum value.
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