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A diet is to contain at least 80 units o...

A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods `F_(1)` and `F_(2)` are available. Food `F_(1)` costs Rs. Rs. 4 per unit food and `F_(2)` costs Rs. 6 per unit. One unit of food`F_(1)` contains 3 units of vitamin A and 4 units of minerals. One unit of food `F_(2)` contains 6 units, of vitamin A and 3 units of minerals, Formulate this as a linear programming problem. Find the minimum cost for diet theat consists of mixture of these two food and also meets the minimal nutritional requirements.

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(Diet Problem): A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain atleast 8 units of vitamin A and 10 units of vitamins C. Food I contains 2 units/ kg of vitamins A and 1 unit/kg of vitamin C. Food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamine C. It costs Rs. 50 per kg to purchase Food I Rs. 70 per kg to purchase Food II. Formulate this problem as a linear programming problem to minimise the cost of such a mixture.