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By P. F. Hsieh, A. W. J. Stoddart

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A. b. What happens to the feasible region? What happens to the optimal objective value? 39] From the results of the previous problem, assuming dz I dbj exists, is it < 0, = 0, or > 0? 39 if the restrictions Ax > b are replaced by Ax b, x > 0 Suppose that a new constraint is added to the problem. a. What happens to the feasible region? b. What happens to the optimal objective value z ? 42] Consider the problem: Minimize ex subject to Ax > b, x > 0 Suppose that a new variable is added to the problem.

Formulate the problem with this added restriction. 5] The technical staff of a hospital wishes to develop a computerized menuplanning system. To start with, a lunch menu is sought. The menu is divided into three major categories: vegetables, meat, and dessert. At least one equivalent serving of each category is desired. 12 Jello Suppose that the minimal requirements of carbohydrates, vitamins, protein, and fats per meal are respectively 5, 10, 10, and 2. a. b. Formulate the menu-planning problem as a linear program.

NOTES AND REFERENCES 1. 2. 3. 4. Linear programming and the simplex method were developed by Dantzig in 1947 in connection with military planning. A great deal of work has influenced the development of linear programming, including World War II operations and the need for scheduling supply and maintenance operations as well as training of Air Force personnel: Leontief s inputoutput model [1951], von Neumann's Equilibrium Model [1937], Koopmans' Model of Transportation [1949], the Hitchcock transportation problem [1941], the work of Kantorovich [1958], von NeumannMorgenstern game theory [1944], and the rapid progress in electronic computing machines have also impacted the field of linear programming.

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