There are n foods and m nutrients. We are given an m x n matrix A, with aijspecifying the amount of nutrient i per unit of the j -th food. Consider a parent with two children. Letb1andb2 be the minimal nutritional requirements of the two children, respectively. Finally, let c be the cost vector with the prices of the different foods. Assume that aij >= 0, andci> 0 for all i and j.

The parent has to buy food to satisfy the children's needs, at minimum cost. To avoid jealousy, there is the additional constraint that the amount to be spent for each child is the same.

1) Provide a standard form formulation of this problem. What are the dimensions of the constraint matrix?

2) If the Dantzig-Wolfe method is used to solve the problem in part (1), construct the subproblems solved during a typical iteration of the master problem.

3) Suggest a direct approach for solving this problem based on the solution of two single-child diet problems.