A dietician wishes to mix two types of foods in such a way that the vitamin content of the mixture contains at least "m" units of vitamin A und "w" units of vitamin C. Food T contains 2 units/kg of vitamin A and 1 unit kg of vitamin C. Food "Ir" contains 1 unit per kg of vitamin A and 2 units per kg of vitamin C. It costs $50 per kg to purchase food "I" and $70 per kg to purchase food "II". Formulate this as a linear progrumming problem and find the minimum cost of such a mixture if it is known that the solution occurs at a comer point (x = 44, y = 12).