A diet is being prepared for the students staying in a hostel. The objective is to feed the students at the least cost meeting the daily requirement of all nutrients as: no less than 8 calories can be starch, no less than 15 calories can be protein and no less than 3 calories can be vitamin. The varied diet is to be made of two foods: A and B. Food A costs $0.60 per kg and contains 11 calories, 4 of which are protein, 2 vitamin and 5 starch. Food B costs $0.35 per kg and contains 10 calories, of which 7 are starch, 2 are protein, and 1 is vitamin.