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Example 6 - A dietician wishes to mix two types of foods

Example 6 - Chapter 12 Class 12 Linear Programming - Part 2
Example 6 - Chapter 12 Class 12 Linear Programming - Part 3
Example 6 - Chapter 12 Class 12 Linear Programming - Part 4
Example 6 - Chapter 12 Class 12 Linear Programming - Part 5
Example 6 - Chapter 12 Class 12 Linear Programming - Part 6
Example 6 - Chapter 12 Class 12 Linear Programming - Part 7

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Transcript

Example 6 (Diet problem): A dietician wishes to mix two types of foods in such away that vitamin contents of the mixture contain atleast 8 units of vitamin A and 10 units of vitamin C. Food ‘I’ contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. Food ‘II’ contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs Rs 50 per kg to purchase Food ‘I’ and Rs 70 per kg to purchase Food ‘II’. Formulate this problem as a linear programming problem to minimise the cost of such a mixture. Let the mixture contain x kg of food I and y kg of food II According to Question : As, we need to minimize the cost of mixture, we will use function minimize Z. Vitamin A Food I contains → 2 units Food II contains → 1 units Total Requirement → atleast 8 units ∴ 2x + y ≥ 8 Vitamin C Food I contains → 1 units Food II contains → 2 units Total Requirement → atleast 10 units ∴ x + 2y ≥ 10 Cost of Food 1 Per Kg = Rs 50 Cost of Food 2 Per kg = Rs 70 ∴ Z = 50 x + 70 y (3) Hence, Combining the constraints : Minimize Z = 50x + 70y Subject to constraints : 2x + y ≥ 8 x + 2y ≥ 10 x, y ≥ 0 Since the feasible region is unbounded, Hence 380 may or may not be the minimum value of z So, we need to graph inequality : 50x + 70y < 380 As, there is no common points between the feasible region inequality. ∴ 380 is the minimum value of z Hence the Optimal mixing strategy would be to mix 2 kg of Food I & 4 kg of Food II , So minimum cost is Rs 380.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.