Consider the problem of nding a minimal cost diet subject to minimum daily requi

ID: 2901234 • Letter: C

Question

Consider the problem of nding a minimal cost diet subject to minimum daily requirements for two

nutrients (vitamins A and K). There are 5 food types for you to choose from, and the 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

(a) Formulate the problem of finding a minimum cost diet meeting the requirements as an LP, and

find an optimal solution for it using the Dual Simplex Method. What is B^-1 for the optimal

solution?

(b) Identify the complementary dual solutions in each of the tableaus in the previous part.

this price competitive with the available foods in meeting this vitamin requirement? Hint: Use

shadow prices.

(d) A delicious new food containing 3 (2) units of vitamin A (K) per unit has become available at a

price of 28 cents/unit. Would you include this food into the optimal diet?

(e) Your favorite grocery story went out of business and you cannot nd food 5 anywhere else. What

is the optimal diet now?

(f) You became concerned with the saturated fat content of your diet. Foods 1 to 5 contain 1,1,0,1

and 2 units of saturated fat, and according to your doctor you are not supposed to consume

more than 20 units of fat a day. How can you incorporate this assumption into your problem

formulation? Is the optimal solution still feasible? What will be your new optimal diet?

a) The required equation would be :

Minimize 20c1 + 20c2 + 31c3 + 11c4 + 12c5 where:

c1 + c3 + c4 + 2c5 >= 21

c2 + 2c3 + c4+ c5 >= 12

& c1,c2,c3,c4,c4 >=0

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