A lab technician has to prepare the following daily diet for rats used in an experiment.  The diet requires a minimum of 600 mg of Vitamin C, 360 mg of Vitamin D, and 40 mg of Vitamin E. The rats should be fed no more than 50 grams per day. One gram of ingredient X contains 20 mg of Vitamin C, 10 mg of Vitamin D, and 4 mg of Vitamin E. One gram of ingredient Y contains 30 mg of Vitamin C, 20 mg of Vitamin D, and 1 mg of Vitamin E. The cost per kg of ingredient X is $5000 and the cost per kg of ingredient Y is $4000. What is the optimal blend of X and Y that minimizes cost?

(1)What are the decision variables for this linear programming problem? 

(2)Write the objective function for this linear programming problem.

(3)Write down all the constraints for this

(4)Graph the constraints and shade the feasible region showing clearly all the corner point  solutions as A,B,C etc. (a clear sketch will do) 

(5)Calculate the X and Y coordinates and cost at each corner point

(6)What is the optimal blend of X and Y at the minimum cost point?