Example 9 - (Diet problem) A dietician has to develop special - Diet problems

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  1. Chapter 12 Class 12 Linear Programming
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Example 9 (Diet problem) A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and at most 300 units of cholesterol. How many packets of each food should be used to minimise the amount of vitamin A in the diet? What is the minimum amount of vitamin A? Let Number of Packets of food P be x Number of Packets of food Q be y According to Question : As, we need to minimize the amount of Vitamin A in diet hence we will use function minimize Z. We need to minimise the amount of vitamin A in the diet Food P Contains → 6 units Vitamin A Food Q Contains → 3 units Vitamin A ∴ Minimize Z = 6x + 3y Combining all the constraints : Minimize Z = 6x + 3y Subject to Constraints, 4x + y ≥ 80, x + 5y ≥ 115, 3x + 2y ≤ 150 , x ≥ 0 , y ≥ 0

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