Food X contains 6 units of Vitamin a per gram and 7 units of vitamin B per gram and costs 12 paise per gram. Food Y contains 8 units of vitamin A per gram and 12 units of vitamin B per gram and costs 20 paise per gram. The daily minimum requirement of vitamin A and vitamin B is 100 units and 120 units. 

a. Formulate the linear programming model for the objective functions and constraints 

b. Use any desired method to find the minimum cost of product mix