This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Morning Hurry — let's get this done. 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. Send me the next one 📸