Ex 12.2, 1 - Chapter 12 Class 12 Linear Programming

Transcript

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 and y kg of food Q According to Question As we need to minimize cost of mixture, the function formed is minimize Z Cost of Food P per kg = Rs 60 Cost of Food Q per kg = Rs 80 ∴ Minimum Cost of Mixture : Minimize 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 380 may or may not be the minimum value of z So, we need to graph inequality : 60x + 80 y < 160 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 at all points joining 𝟖﷮𝟑﷯, 0﷯ & 𝟐, 𝟏﷮𝟐﷯﷯