Let the problem of finding the minimal cost diet subject to minimum daily needs for 2 nutrients (vitamins A and K). There are 5 food kinds for you to select from, and requirements are as follows:

Nutrient Nutrient units/unit food MDR for nutrient

1 2 3 4 5

vitaminA 1 0 1 1 2 21

vitaminK 0 1 2 1 1 12

cost (cents/unit) 20 20 31 11 12

i) Formulate problem of finding the minimum cost diet meeting needs as LP, and find optimal solution for it using Dual Simplex Method. Find B^-1 for optimal solution?

ii) Find complementary dual solutions in each of tableaus in previous part.

iii) The local pharmacist is selling vitamin K pills at the cost of 12 cents/unit of vitamin K content. Is the price competitive with available foods in meeting this vitamin requirement?

iv) The delicious new food containing 3 (2) units of vitamin A (K) per unit has become available at the price of 28 cents/unit. Would you include the food into optimal diet?

(e) The favorite grocery story went out of business and you can't find food five anywhere else. Find optimal diet now?

(f) You became concerned with saturated fat content of the diet. Foods 1 to 5 has 1,1,0,1 and 2 units of saturated fat, and according to the doctor you are not supposed to consume more than twenty units of fat a day. How can you include assumption into the problem formulation? Is optimal solution still feasible? Find new optimal diet?