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 gramsof 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 companymakes 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? Whais the maximum daily profit? Summarize the model,MaximizeObjective functionsubject toV 36,000Sulfur dioxide constraintV 90,000Particulate constraintх, у 2Nonnegative constraintUnder the stated government regulations a maximum profit of $ is obtained by producingof product using the old process andof 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 theconstraints 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 andV 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 andof product using the new process.Enter your answer in each of the answer boxes.

Name: Because of new federal regulations on pollution, a chemical plant int
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: 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 gramsof sulfur dioxide

let the gallon produced by older process =x let the gallon produced by new process =y according to question older process emitted sulphur dioxide =40 gramsparticulate matter =120 grams new process emitted sulphur dioxide =5 gramsparticulate matter =40 grams (a) not more than 36,000 grams of sulphur dioxide and 90,000 grams of particulate matter is allowed we get, 40x+5y≤36,000⇒8x+y≤7200 ...i 120x+40y≤90,000⇒3x+y≤2250 ...ii according to question , the company makes a profit of 80 cent per gallon and 20 cent per gallon the profit function is Z=80x+20y that is , objective function Z=80x+20y subject to 8x+y≤72003x+y≤2250 with x≥0,y≥0we will solve the inequality graphically we will get three points on the boundary of required region 0,7200 , 0,2250 , 990,-720 now we will calculate at which point the profit is maximum Z=80x+20y put x=0 , y=7200 Z=80×0+20×7200 =144000 put x=0 , y=2250 Z=80×0+20×2250 =45000 put x=990 , y=-720 Z=80×990+20×-720 =79200-14400 =64800 hence we get maximum profit of $ 144000 by producing 0 gallon by old process and 7200 gallon by new process