A factory produces two pesticides, A and B. Pesticide A produces 0.25 kg CO and 0.60 kg SO2 per barrel…

Question

A factory produces two pesticides, A and B. Pesticide A produces 0.25 kg CO and 0.60 kg SO2 per barrel. Pesticide B produces 0.60 kg CO and 0.20 kg SO2 per barrel. The factory has a maximum of 75 kg C

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Let x be the number of barrels of pesticide A produced per day. Let y be the number of barrels of pesticide B produced per day. Q2: Find a System of inequality Step 1: Identify the emissions for each pesticide and the daily limits. Pesticide A: 0.25 kg CO, 0.60 kg SO₂ per barrel. Pesticide B: 0.60 kg CO, 0.20 kg SO₂ per barrel. Maximum CO emission: 75 kg per day. Maximum SO₂ emission: 90 kg per day. Step 2: Formulate the inequalities based on the total emissions. The total CO emission must be less than or equal to 75 kg: 0.25x + 0.60y ≤ 75 The total SO₂ emission must be less than or equal to 90 kg: 0.60x + 0.20y ≤ 90 Since the number of barrels cannot be negative: x ≥ 0 y ≥ 0 The system of inequalities is: 0.25x + 0.60y ≤ 75 0.60x + 0.20y ≤ 90 x ≥ 0 y ≥ 0 (Note: Graphing the feasible region is not possible in this text-based format.) Q3: Would it be legal for the factory to produce 100 barrels of A and 80 barrels of B per day? Step 1: Substitute x = 100 and y = 80 into the CO emission inequality. 0.25(100) + 0.60(80) ≤ 75 25 + 48 ≤ 75 73 ≤ 75 This inequality holds true. Step 2: Substitute x = 100 and y = 80 into the SO₂ emission inequality. 0.60(100) + 0.20(80) ≤ 90 60 + 16 ≤ 90 76 ≤ 90 This inequality also holds true. Since both pollution constraints are satisfied, it would be legal. The answer is: Yes, it would be legal. Q4: Would it be legal for the factory to produce 60 barrels of A and 160 barrels of B per day? Step 1: Substitute x = 60 and y = 160 into the CO emission inequality. 0.25(60) + 0.60(160) ≤ 75 15 + 96 ≤ 75 111 ≤ 75 This inequality is false (111 is not less than or equal to 75). Step 2: Substitute x = 60 and y = 160 into the SO₂ emission inequality. 0.60(60) + 0.20(160) ≤ 90 36 + 32 ≤ 90 68 ≤ 90 This inequality holds true. Since the CO emission constraint is violated, it would not be legal. The answer is: No, it would not be legal.

A factory produces two pesticides, A and B. Pesticide A produces 0.25 kg CO and 0.60 kg SO2 per barrel. Pesticide B produces 0.60 kg CO and 0.20 kg SO2 per barrel. The factory has a maximum of 75 kg C

Step-by-step solution

Identify the emissions for each pesticide and the daily limits.

Formulate the inequalities based on the total emissions.

Substitute $x = 100$ and $y = 80$ into the CO emission inequality.

Substitute $x = 100$ and $y = 80$ into the SO₂ emission inequality.

Substitute $x = 60$ and $y = 160$ into the CO emission inequality.

Substitute $x = 60$ and $y = 160$ into the SO₂ emission inequality.

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More Mathematics Questions

A factory produces two pesticides, A and B. Pesticide A produces 0.25 kg CO and 0.60 kg SO2 per barrel. Pesticide B produces 0.60 kg CO and 0.20 kg SO2 per barrel. The factory has a maximum of 75 kg C

Step-by-step solution

Identify the emissions for each pesticide and the daily limits.

Formulate the inequalities based on the total emissions.

Substitute x=100x = 100x=100 and y=80y = 80y=80 into the CO emission inequality.

Substitute x=100x = 100x=100 and y=80y = 80y=80 into the SO₂ emission inequality.

Substitute x=60x = 60x=60 and y=160y = 160y=160 into the CO emission inequality.

Substitute x=60x = 60x=60 and y=160y = 160y=160 into the SO₂ emission inequality.

Still stuck on this one?

More Mathematics Questions

Substitute $x = 100$ and $y = 80$ into the CO emission inequality.

Substitute $x = 100$ and $y = 80$ into the SO₂ emission inequality.

Substitute $x = 60$ and $y = 160$ into the CO emission inequality.

Substitute $x = 60$ and $y = 160$ into the SO₂ emission inequality.