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Ex 12.2, 1 Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs 80/kg. Food P contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while food Q contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.Let the mixture contain x kg of food P & y kg of food Q According to Question Also, we need to minimize cost of mixture, Cost of Food P per kg = Rs 60 Cost of Food Q per kg = Rs 80 Vitamin A Food P contains → 3 units Food Q contains → 4 units Total Requirement → Atleast 8 units ∴ 3x + 4y ≥ 8 Vitamin B Food P contains → 5 units Food Q contains → 2 units Total Requirement → Atleast 11 units ∴ 5x + 2y ≥ 11 ∴ Cost of Mixture: Z = 60x + 80 y Hence, Combining the constraints : Minimize Z = 60x + 80 y Subject to constraints 3x + 4y ≥ 8 5x + 2y ≥ 11 x ≥ 0, y ≥ 0 Since the feasible region is unbounded, Hence, 160 may or may not be the minimum value of z So, we need to graph inequality : Z < 160 60x + 80 y < 160 3x + 4y < 8 Graphing 3x + 4y < 8 As, there is no common points between the feasible region inequality. ∴ 160 is the minimum value of Z Since, Z is minimum at two points (8/3 ", 0" ) & (2, 1/2) Hence, Minimum cost of mixture is Rs 160 and at all points joining (𝟖/𝟑 ", 0" ) & (𝟐,𝟏/𝟐)

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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.