Exam 10: Integer Programming, Goal Programming, and Nonlinear Programming

Consider the following 0-1 integer programming problem: Minimize 20X + 36Y +24Z Subject to: 2X + 4Y + 3Z ≥ 7 12X + 8Y + 10Z ≥ 25 X, Y, Z must be 0 or 1 If we wish to add the constraint that no more than two of these variables must be positive, how would this be written?

An integer programming (maximization)problem was first solved as a linear programming problem, and the objective function value (profit)was $253.67.The two decision variables (X, Y)in the problem had values of X = 12.45 and Y = 32.75.If there is a single optimal solution, which of the following must be true for the optimal integer solution to this problem?

The constraint X₁ - X₂ = 0 with 0 -1 integer programming allows for either both X₁ and X₂ to be selected to be a part of the optimal solution, or for neither to be selected.

An integer programming (minimization)problem was first solved as a linear programming problem, and the objective function value (cost)was $253.67.The two decision variables (X, Y)in the problem had values of X = 12.45 and Y = 32.75.If there is a single optimal solution, which of the following must be true for the optimal integer solution to this problem?

A bakery produces muffins and doughnuts.Let x₁ be the number of doughnuts produced and x₂ be the number of muffins produced.The profit function for the bakery is expressed by the following equation: profit = 4x₁ + 2x₂ + 0.3x₁² + 0.4x₂².The bakery has the capacity to produce 800 units of muffins and doughnuts combined and it takes 30 minutes to produce 100 muffins and 20 minutes to produce 100 doughnuts.There is a total of 4 hours available for baking time.There must be at least 200 units of muffins and at least 200 units of doughnuts produced.How many doughnuts and muffins should the bakery produce in order to maximize profit?

Terms that are minimized in goal programming are called