1. (25%) Consider the diet problem with the following data involving two nutrients (vitamins A, I<) with minimum daily requirements (MDR), and 5 different foods.
Nutrient Nutrient unitslunit food MDR for
1 2 3 4 5 nutrient
Vitamin A 1 0 1 1 2 2 1
Vitamin K 0 1 2 1 1 12
Cost (centslunit) 20 20 3 1 11 12
(a) (5%) Formulate the problem of finding a minimum cost diet meeting the requirements.
(b) (5%) Find an optimum solution for the problem. Let x and B denote
the optimum solution and basis obtained, respectively.
(c) (5%) For what range of values of c4 (costlunit of food 4) is the current
optimal solution x remains optimal?
(d) (5%) For what range of values of the MDR of vitamin K (whose present
value is 12) does the basis 3 remain optimal t o the problem?
(e) (2%) A local pharmacist is selling vitamin K pills at a cost of 12 centslunit of
vitamin K content. Is this price competitive with the available foods in meeting
this vitamin requirement?
(f) (3%) A delicious new food containing 3, 2 units of vitamins A, K respectively
per unit has become available at a price of 28 centslunit. How much is the urge
t o include at least 1 unit of this in the daily diet going t o cost, over a minimum
cost diet?
2. (10%) Construct a system of constraints including binary variables if necessary
whose feasible region is { ( x , , ~ , ] : 5 I X, 110,5 I x2 < 10).
3. (15%) Four customers are bidding for four valuable paintings. Customer 2 is
willing t o buy t w o paintings, but each other customer is willing t o purchase at most one painting. The prices that each customer is willing t o pay are given in the following table. Determine how t o maximize the total revenue received from the sale of the paintings by the Hungarian method.
Bid for ($)
Customer
Painting 1 Painting 2 Painting 3 Painting 4
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