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 and "n" 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 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 programming problem and find the minimum cost of such a mixture if it is known that the solution occurs at a corner point (x = 5, y = 22