A farmer plans to mix two types food to make a mix of low cost feed for animals in his farm. A bag of food A costs $10 and contains 40 units of protein, 20 units of minerals and 10 units of vitamins. A bag of food B costs $12 and contains 30 units of protein, 20 units of minerals and 30 units of vitamins. How many bags of food A and food B should be consumed by animals each day in order to meet the minimum daily requirements of 200 units of protein, 120 units of minerals and 100 units of vitamins at a minimum cost? (a) Formulate this optimization problem as a Linear Programming Problem. (b) Show the feasible region, find all extreme points and solve the problem graphically. (c) Use graphical sensitivity analysis to show that if the cost of one bag of food A is between $4 and $12, the current basis remains optimal. (d) What would be the new optimal solution if the cost of each bag of food A is $15?