We consider buying three kinds of food. food i has 1 unit of vitamin a, 3 units of vitamin b, and 4 units of vitamin c. food ii has 2, 3, and 5 units, respectively and food iii has 3, 0 and 3 units, respectively. we need to have 11 units of vitamins a, 9 of vitamin b, and 20 of vitamin c.
(a) find all possible amounts of three foods that will provide precisely these amounts of vitamins.
(b) if food i costs 60 cents and the others cost 10 cents each per unit, is there a solution costing exactly 100 cents.