Question

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.

Answer 1

`1\dotplus 2* 2\dotplus 3* 2\\3\dotplus 3* 2\dotplus 0* 2\\4\dotplus 5* 2\dotplus 3* 2` 1\dotplus 2\times 2\dotplus 3\times 2

Explanation:

we will take 1 times unit of A from food 1 and 2 times of unit of A from second food and 2 times unit from third

similarly for B we take 1times unit from food 1 and 2times unit from second and 2 times of unit from third

then we get desired A=11,B=9,C=20