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1. Chapter 12 Class 12 Linear Programming
2. Serial order wise
3. Miscellaneous

Transcript

Misc 1 Refer to Example 9. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet? Let Number of Packets of food P be x Number of Packets of food Q be y According to Question : As, we need to maximize the amount of Vitamin A in diet hence we will use function maximize Z. Calcium P contains → 12 units Q contains → 3 units Total Requirement → atleast 240 units ∴ 12x + 3y ≥ 240 4x + y ≥ 80 Iron P contains → 4 units Q contains → 20 units Total Requirement → at least 460 units ∴ 4x + 20y ≥ 460 x + 5y ≥ 115 Cholesterol P contains → 6 units Q contains → 4 units Total Requirement → At most 300 ∴ 6x + 4y ≤ 300 3x + 2y "≤" 150 We need to maximize the amount of vitamin A in the diet Food P Contains → 6 units Vitamin A Food Q Contains → 3 units Vitamin A ∴ Maximize Z = 6x + 3y Combining all the constraints : Maximize Z = 6x + 3y Subject to Constraints, 4x + y ≥ 80, x + 5y ≥ 115, 3x + 2y ≤ 150, x ≥ 0 , y ≥ 0 Hence, the amount of Vitamin A will be maximum if 40 Packets of Food P & 15 Packets of Food Q are Used. Thus, maximum amount of Vitamin A = 285 Units

Miscellaneous 