A dietitian prepares a special diet using two food groups, A and B. Each ounce of food group A contains 3 units of vitamin C and 1 unit of vitamin D. Each ounce of food group B contains 1 unit of vitamin C and 2 units of vitamin D. The minimum daily requirements with this diet are at least 9 units of vitamin C and at least 8 units of vitamin D. Each ounce of food group A costs 50 cents, and each ounce of food group B costs 30 cents. 

(a) List the constraints. 

(b) Determine the objective function for minimizing cost.

(c) Graph the set of constraints. 

(d) Determine the vertices of the feasible region.

(e) How many ounces of each food group should be used to meet the daily requirements and minimize the cost?

(f)  Determine the minimum cost.